Using Entity Framework 5, Visual Studio 2010 with the Entity Framework Power Tools (Beta 2) extension.
Here is my database table structure:

I used the Reverse Engineer Code First function of the aforementioned extension, which generated the POCO classes and some 'mapping' files (not sure if that's the formal parlance) and a single DbContext-derived class. Other than the change I describe next, all of these generated classes are as-generated by the power tool.
In the Category.cs file, I added the following code to help flatten the object graph a bit:
private ICollection<Product> m_Products = null;
public ICollection<Product> Products
{
    get
    {
        if (m_Products == null)
        {
            m_Products = new List<Product>();
            foreach (var categoryProduct in CategoryProducts)
            {
                m_Products.Add(categoryProduct.Product);
            }
        }
        return m_Products;
    }
    set { m_Products = value; }
}
I get the following exception, which I know must have something to do with the mappings, but I just can't quite figure this out.
Unhandled Exception: System.Data.EntityCommandExecutionException: An error occurred while 
executing the command definition. See the inner exception for details.
 ---> System.Data.SqlClient.SqlException: 
      Invalid column name 'Category_CategoryId'.
If I need to post more information, such as the specifics of the mappings, just let me know and I'll do it. I wanted to keep this as short as possible, but I realize I've omitted some things that, for those unfamiliar with the code generated by the tool, may leave one wanting for more details.