For built-in types, you can use the TypeCode enumeration.  Please note that GetType() is kind of slow, but probably not relevant in most situations.
switch (Type.GetTypeCode(someObject.GetType()))
{
    case TypeCode.Boolean:
        break;
    case TypeCode.Byte:
        break;
    case TypeCode.Char:
        break;
}
For custom types, you can create your own enumeration, and either an interface or a base class with abstract property or method...
Abstract class implementation of property
public enum FooTypes { FooFighter, AbbreviatedFool, Fubar, Fugu };
public abstract class Foo
{
    public abstract FooTypes FooType { get; }
}
public class FooFighter : Foo
{
    public override FooTypes FooType { get { return FooTypes.FooFighter; } }
}
Abstract class implementation of method
public enum FooTypes { FooFighter, AbbreviatedFool, Fubar, Fugu };
public abstract class Foo
{
    public abstract FooTypes GetFooType();
}
public class FooFighter : Foo
{
    public override FooTypes GetFooType() { return FooTypes.FooFighter; }
}
Interface implementation of property
public enum FooTypes { FooFighter, AbbreviatedFool, Fubar, Fugu };
public interface IFooType
{
    FooTypes FooType { get; }
}
public class FooFighter : IFooType
{
    public FooTypes FooType { get { return FooTypes.FooFighter; } }
}
Interface implementation of method
public enum FooTypes { FooFighter, AbbreviatedFool, Fubar, Fugu };
public interface IFooType
{
    FooTypes GetFooType();
}
public class FooFighter : IFooType
{
    public FooTypes GetFooType() { return FooTypes.FooFighter; }
}
One of my coworkers just told me about this too: This has the advantage that you can use it for literally any type of object, not just ones that you define.  It has the disadvantage of being a bit larger and slower.
First define a static class like this:
public static class TypeEnumerator
{
    public class TypeEnumeratorException : Exception
    {
        public Type unknownType { get; private set; }
        public TypeEnumeratorException(Type unknownType) : base()
        {
            this.unknownType = unknownType;
        }
    }
    public enum TypeEnumeratorTypes { _int, _string, _Foo, _TcpClient, };
    private static Dictionary<Type, TypeEnumeratorTypes> typeDict;
    static TypeEnumerator()
    {
        typeDict = new Dictionary<Type, TypeEnumeratorTypes>();
        typeDict[typeof(int)] = TypeEnumeratorTypes._int;
        typeDict[typeof(string)] = TypeEnumeratorTypes._string;
        typeDict[typeof(Foo)] = TypeEnumeratorTypes._Foo;
        typeDict[typeof(System.Net.Sockets.TcpClient)] = TypeEnumeratorTypes._TcpClient;
    }
    /// <summary>
    /// Throws NullReferenceException and TypeEnumeratorException</summary>
    /// <exception cref="System.NullReferenceException">NullReferenceException</exception>
    /// <exception cref="MyProject.TypeEnumerator.TypeEnumeratorException">TypeEnumeratorException</exception>
    public static TypeEnumeratorTypes EnumerateType(object theObject)
    {
        try
        {
            return typeDict[theObject.GetType()];
        }
        catch (KeyNotFoundException)
        {
            throw new TypeEnumeratorException(theObject.GetType());
        }
    }
}
And then you can use it like this:
switch (TypeEnumerator.EnumerateType(someObject))
{
    case TypeEnumerator.TypeEnumeratorTypes._int:
        break;
    case TypeEnumerator.TypeEnumeratorTypes._string:
        break;
}