Foreword
There's a 2.8 collection walk-through by Martin Odersky which should probably be your first reference. It has been supplemented as well with architectural notes, which will be of particular interest to those who want to design their own collections. 
The rest of this answer was written way before any such thing existed (in fact, before 2.8.0 itself was released).
You can find a paper about it as Scala SID #3. Other papers in that area should be interesting as well to people interested in the differences between Scala 2.7 and 2.8.
I'll quote from the paper, selectively, and complement with some thoughts of mine. There are also some images, generated by Matthias at decodified.com, and the original SVG files can be found here.
The collection classes/traits themselves
There are actually three hierarchies of traits for the collections: one for mutable collections, one for immutable collections, and one which doesn't make any assumptions about the collections.
There's also a distinction between parallel, serial and maybe-parallel collections, which was introduced with Scala 2.9. I'll talk about them in the next section. The hierarchy described in this section refers exclusively to non-parallel collections.
The following image shows the non-specific hierarchy introduced with Scala 2.8:

All elements shown are traits. In the other two hierarchies there are also classes directly inheriting the traits as well as classes which can be viewed as belonging in that hierarchy through implicit conversion to wrapper classes. The legend for these graphs can be found after them.
Graph for immutable hierarchy:

Graph for mutable hierarchy:

Legend:

Here's an abbreviated ASCII depiction of the collection hierarchy, for those who can't see the images.
                    Traversable
                         |
                         |
                      Iterable
                         |
      +------------------+--------------------+
     Map                Set                  Seq
      |                  |                    |
      |             +----+----+         +-----+------+
    Sorted Map  SortedSet   BitSet   Buffer Vector LinearSeq
Parallel Collections
When Scala 2.9 introduced parallel collections, one of the design goals was to make their use as seamless as possible. In the simplest terms, one can replace a non-parallel (serial) collection with a parallel one, and instantly reap the benefits.
However, since all collections until then were serial, many algorithms using them assumed and depended on the fact that they were serial. Parallel collections fed to the methods with such assumptions would fail. For this reason, all the hierarchy described in the previous section mandates serial processing.
Two new hierarchies were created to support the parallel collections.
The parallel collections hierarchy has the same names for traits, but preceded with Par: ParIterable, ParSeq, ParMap and ParSet. Note that there is no ParTraversable, since any collection supporting parallel access is capable of supporting the stronger ParIterable trait. It doesn't have some of the more specialized traits present in the serial hierarchy either. This whole hierarchy is found under the directory scala.collection.parallel.
The classes implementing parallel collections also differ, with ParHashMap and ParHashSet for both mutable and immutable parallel collections, plus ParRange and ParVector implementing immutable.ParSeq and ParArray implementing mutable.ParSeq.
Another hierarchy also exists that mirrors the traits of serial and parallel collections, but with a prefix Gen: GenTraversable, GenIterable, GenSeq, GenMap and GenSet. These traits are parents to both parallel and serial collections. This means that a method taking a Seq cannot receive a parallel collection, but a method taking a GenSeq is expected to work with both serial and parallel collections.
Given the way these hierarchies were structured, code written for Scala 2.8 was fully compatible with Scala 2.9, and demanded serial behavior. Without being rewritten, it cannot take advantage of parallel collections, but the changes required are very small.
Using Parallel Collections
Any collection can be converted into a parallel one by calling the method par on it. Likewise, any collection can be converted into a serial one by calling the method seq on it.
If the collection was already of the type requested (parallel or serial), no conversion will take place. If one calls seq on a parallel collection or par on a serial collection, however, a new collection with the requested characteristic will be generated.
Do not confuse seq, which turns a collection into a non-parallel collection, with toSeq, which returns a Seq created from the elements of the collection. Calling toSeq on a parallel collection will return a ParSeq, not a serial collection.
The Main Traits
While there are many implementing classes and subtraits, there are some basic traits in the hierarchy, each of which providing more methods or more specific guarantees, but reducing the number of classes that could implement them.
In the following subsections, I'll give a brief description of the main traits and the idea behind them.
Trait TraversableOnce
This trait is pretty much like trait Traversable described below, but with the limitation that you can only use it once. That is, any methods called on a TraversableOnce may render it unusable.
This limitation makes it possible for the same methods to be shared between the collections and Iterator. This makes it possible for a method that works with an Iterator but not using Iterator-specific methods to actually be able to work with any collection at all, plus iterators, if rewritten to accept TraversableOnce.
Because TraversableOnce unifies collections and iterators, it does not appear in the previous graphs, which concern themselves only with collections.
Trait Traversable
At the top of the collection hierarchy is trait Traversable. Its only abstract operation is
def foreach[U](f: Elem => U)
The operation is meant to traverse all elements of the collection, and apply the given operation f to each
element. The application is done for its side effect only; in fact any function result of f is discarded by
foreach.
Traversible objects can be finite or infinite. An example of an infinite traversable object is the stream
of natural numbers Stream.from(0). The method hasDefiniteSize indicates whether a collection is possibly
infinite. If hasDefiniteSize returns true, the collection is certainly finite. If it returns false, the
collection has not been not fully elaborated yet, so it might be infinite or finite.
This class defines methods which can be efficiently implemented in terms of foreach (over 40 of them).
Trait Iterable
This trait declares an abstract method iterator that returns an iterator that yields all the collection’s elements one by one. The foreach method in Iterable is implemented in terms of iterator. Subclasses of Iterable often override foreach with a direct implementation for efficiency.
Class Iterable also adds some less-often used methods to Traversable, which can be implemented efficiently only if an iterator is available. They are summarized below.
xs.iterator          An iterator that yields every element in xs, in the same order as foreach traverses elements.
xs takeRight n       A collection consisting of the last n elements of xs (or, some arbitrary n elements, if no order is defined).
xs dropRight n       The rest of the collection except xs takeRight n.
xs sameElements ys   A test whether xs and ys contain the same elements in the same order
Other Traits
After Iterable there come three base traits which inherit from it: Seq, Set, and Map. All three have an apply method and all three implement the PartialFunction trait, but the meaning of apply is different in each case.
I trust the meaning of Seq, Set and Map is intuitive. After them, the classes break up in specific implementations that offer particular guarantees with regards to performance, and the methods it makes available as a result of it. Also available are some traits with further refinements, such as LinearSeq, IndexedSeq and SortedSet.
The listing below may be improved. Leave a comment with suggestions and I'll fix it.
Base Classes and Traits
- Traversable-- Basic collection class. Can be implemented just with- foreach.- 
- TraversableProxy-- Proxy for a- Traversable. Just point- selfto the real collection.
- TraversableView-- A Traversable with some non-strict methods.
- TraversableForwarder-- Forwards most methods to- underlying, except- toString,- hashCode,- equals,- stringPrefix,- newBuilder,- viewand all calls creating a new iterable object of the same kind.
- mutable.Traversableand- immutable.Traversable-- same thing as- Traversable, but restricting the collection type.
- Other special-cases Iterableclasses, such asMetaData, exists.
- Iterable-- A collection for which an- Iteratorcan be created (through- iterator).- 
- IterableProxy,- IterableView,- mutableand- immutable.Iterable.
 
 
- Iterator-- A trait which is not descendant of- Traversable. Define- nextand- hasNext.- 
- CountedIterator-- An- Iteratordefining- count, which returns the elements seen so  far.
- BufferedIterator-- Defines- head, which returns the next element without consuming it.
- Other special-cases Iteratorclasses, such asSource, exists.
 
The Maps
- Map-- An- Iterableof- Tuple2, which also provides methods for retrieving a value (the second element of the tuple) given a key (the first element of the tuple). Extends- PartialFunctionas well.- 
- MapProxy-- A- Proxyfor a- Map.
- DefaultMap-- A trait implementing some of- Map's abstract methods.
- SortedMap-- A- Mapwhose keys are sorted.- 
- immutable.SortMap- 
- immutable.TreeMap-- A class implementing- immutable.SortedMap.
 
 
- immutable.Map- 
- immutable.MapProxy
- immutable.HashMap-- A class implementing- immutable.Mapthrough key hashing.
- immutable.IntMap-- A class implementing- immutable.Mapspecialized for- Intkeys. Uses a tree based on the binary digits of the keys.
- immutable.ListMap-- A class implementing- immutable.Mapthrough lists.
- immutable.LongMap-- A class implementing- immutable.Mapspecialized for- Longkeys. See- IntMap.
- There are additional classes optimized for an specific number of elements.
 
- mutable.Map- 
- mutable.HashMap-- A class implementing- mutable.Mapthrough key hashing.
- mutable.ImmutableMapAdaptor-- A class implementing a- mutable.Mapfrom an existing- immutable.Map.
- mutable.LinkedHashMap-- ?
- mutable.ListMap-- A class implementing- mutable.Mapthrough lists.
- mutable.MultiMap-- A class accepting more than one distinct value for each key.
- mutable.ObservableMap-- A mixin which, when mixed with a- Map, publishes events to observers through a- Publisherinterface.
- mutable.OpenHashMap-- A class based on an open hashing algorithm.
- mutable.SynchronizedMap-- A mixin which should be mixed with a- Mapto provide a version of it with synchronized methods.
- mutable.MapProxy.
 
 
The Sequences
- Seq-- A sequence of elements. One assumes a well-defined size and element repetition. Extends- PartialFunctionas well.- 
- IndexedSeq-- Sequences that support O(1) element access and O(1) length computation.- 
- IndexedSeqView
- immutable.PagedSeq-- An implementation of- IndexedSeqwhere the elements are produced on-demand by a function passed through the constructor.
- immutable.IndexedSeq- 
- immutable.Range-- A delimited sequence of integers, closed on the lower end, open on the high end, and with a step.- 
- immutable.Range.Inclusive-- A- Rangeclosed on the high end as well.
- immutable.Range.ByOne-- A- Rangewhose step is 1.
 
- immutable.NumericRange-- A more generic version of- Rangewhich works with any- Integral.- 
- immutable.NumericRange.Inclusive,- immutable.NumericRange.Exclusive.
- immutable.WrappedString,- immutable.RichString-- Wrappers which enables seeing a- Stringas a- Seq[Char], while still preserving the- Stringmethods. I'm not sure what the difference between them is.
 
 
- mutable.IndexedSeq- 
- mutable.GenericArray-- An- Seq-based array-like structure. Note that the "class"- Arrayis Java's- Array, which is more of a memory storage method than a class.
- mutable.ResizableArray-- Internal class used by classes based on resizable arrays.
- mutable.PriorityQueue,- mutable.SynchronizedPriorityQueue-- Classes implementing prioritized queues -- queues where the elements are dequeued according to an- Orderingfirst, and order of queueing last.
- mutable.PriorityQueueProxy-- an abstract- Proxyfor a- PriorityQueue.
 
 
- LinearSeq-- A trait for linear sequences, with efficient time for- isEmpty,- headand- tail.- 
- immutable.LinearSeq- 
- immutable.List-- An immutable, singlely-linked, list implementation.
- immutable.Stream-- A lazy-list. Its elements are only computed on-demand, but memoized (kept in memory) afterwards. It can be theoretically infinite.
 
- mutable.LinearSeq- 
- mutable.DoublyLinkedList-- A list with mutable- prev,- head(- elem) and- tail(- next).
- mutable.LinkedList-- A list with mutable- head(- elem) and- tail(- next).
- mutable.MutableList-- A class used internally to implement classes based on mutable lists.- 
- mutable.Queue,- mutable.QueueProxy-- A data structure optimized for FIFO (First-In, First-Out) operations.
- mutable.QueueProxy-- A- Proxyfor a- mutable.Queue.
 
 
 
- SeqProxy,- SeqView,- SeqForwarder
- immutable.Seq- 
- immutable.Queue-- A class implementing a FIFO-optimized (First-In, First-Out) data structure. There is no common superclass of both- mutableand- immutablequeues.
- immutable.Stack-- A class implementing a LIFO-optimized (Last-In, First-Out) data   structure. There is no common superclass of both- mutable- immutablestacks.
- immutable.Vector-- ?
- scala.xml.NodeSeq-- A specialized XML class which extends- immutable.Seq.
- immutable.IndexedSeq-- As seen above.
- immutable.LinearSeq-- As seen above.
 
- mutable.ArrayStack-- A class implementing a LIFO-optimized data structure using arrays. Supposedly significantly faster than a normal stack.
- mutable.Stack,- mutable.SynchronizedStack-- Classes implementing a LIFO-optimized data structure.
- mutable.StackProxy-- A- Proxyfor a- mutable.Stack..
- mutable.Seq- 
- mutable.Buffer-- Sequence of elements which can be changed by appending, prepending or inserting new members.- 
- mutable.ArrayBuffer-- An implementation of the- mutable.Bufferclass, with constant amortized time for the append, update and random access operations. It has some specialized subclasses, such as- NodeBuffer.
- mutable.BufferProxy,- mutable.SynchronizedBuffer.
- mutable.ListBuffer-- A buffer backed by a list. It provides constant time append and prepend, with most other operations being linear.
- mutable.ObservableBuffer-- A mixin trait which, when mixed to a- Buffer, provides notification events through a- Publisherinterfaces.
- mutable.IndexedSeq-- As seen above.
- mutable.LinearSeq-- As seen above.
 
 
 
The Sets
- Set-- A set is a collection that includes at most one of any object.- 
- BitSet-- A set of integers stored as a bitset.- 
- immutable.BitSet
- mutable.BitSet
 
- SortedSet-- A set whose elements are ordered.- 
- immutable.SortedSet- 
- immutable.TreeSet-- An implementation of a- SortedSetbased on a tree.
 
 
- SetProxy-- A- Proxyfor a- Set.
- immutable.Set- 
- immutable.HashSet-- An implementation of- Setbased on element hashing.
- immutable.ListSet-- An implementation of- Setbased on lists.
- Additional set classes exists to provide optimized implementions for sets from 0 to 4 elements.
- immutable.SetProxy-- A- Proxyfor an immutable- Set.
 
- mutable.Set- 
- mutable.HashSet-- An implementation of- Setbased on element hashing.
- mutable.ImmutableSetAdaptor-- A class implementing a mutable- Setfrom an immutable- Set.
- LinkedHashSet-- An implementation of- Setbased on lists.
- ObservableSet-- A mixin trait which, when mixed with a- Set, provides notification events through a- Publisherinterface.
- SetProxy-- A- Proxyfor a- Set.
- SynchronizedSet-- A mixin trait which, when mixed with a- Set, provides notification events through a- Publisherinterface.
 
 
- Why the Like classes exist (e.g. TraversableLike)
This was done to achieve maximum code reuse. The concrete generic implementation for classes with a certain structure (a traversable, a map, etc) is done in the Like classes. The classes intended for general consumption, then, override selected methods that can be optmized.
- What the companion methods are for (e.g. List.companion)
The builder for the classes, ie, the object which knows how to create instances of that class in a way that can be used by methods like map, is created by a method in the companion object. So, in order to build an object of type X, I need to get that builder from the companion object of X. Unfortunately, there is no way, in Scala, to get from class X to object X. Because of that, there is a method defined in each instance of X, companion, which returns the companion object of class X.
While there might be some use for such method in normal programs, its target is enabling code reuse in the collection library.
- How I know what implicit objects are in scope at a given point
You aren't supposed to care about that. They are implicit precisely so that you don't need to figure out how to make it work.
These implicits exists to enable the methods on the collections to be defined on parent classes but still return a collection of the same type. For example, the map method is defined on TraversableLike, but if you used on a List you'll get a List back.