You have the bulk of it already! I may not get every single one, but here goes:
E-flat : tiny, high. The super-soprano of the band.
B-flat : your basic, garden variety clarinet. Used in both band and orchestra.
A : Similar to B-flat, but some orchestra music calls for the A. If you have both it beats the hell out of transposing your part!
E-flat alto: Neither fish nor foul, plays in the middle range.
B-flat bass: The basic big clarinet - I've never played one, but they look like lots of fun!
Contrabass: Even bigger than the bass!
There are also others with purposes I am not sure of: like:
C clarinet - Popular in Europe, but not sure of the application.
There may be some others that I don't know about!