Ok let's create a list of the pieces that all clarinet players should learn, hopefully it'll provide you with some inspiration.
I'll start here:
Mozart's Clarinet Concerto in A, 3rd Movement. Absolute classic. Preferably on an A-clarinet, where available (unfortunately the one at my school was nicked, most likely by someone at a neighbouring school which has mysteriosly acquired one!). Bonus points if you can play it in the right key on a Bb clarinet!
For concerti, Weber's pair(#1, #2) and the Nielsen are the only ones I know other than the Mozart. All three are great, but good luck to anyone trying to learn them - they sound pretty hard!
For chamber music, the Brahms sonatas (#1, #2) are absolutely fantastic. Also, if you can find arrangements for clarinet and piano (or if you have any willing string players handy) Brahms' trio and quintet, and Mozart's quintet are deservedly repertoire standards. (I think there's actually a clarinet/piano arrangement of the Mozart quintet on IMSLP).
Beethoven's clarinet trio is a favourite of mine( 'No 4 - 'Gassenhauer'), and the arrangement of the Septet for trio. Both, like the Brahms, have a rather demanding piano part. Quite like one of the sonatas, really.
Finzi and Copland have their concerti, which are rather good. Copland's was written for Benny Goodman, who couldn't play the coda.
(Original post by j.alexanderh)
All three are great, but good luck to anyone trying to learn them - they sound pretty hard!
The Weber pair, especially the second, which is quite high, and ends with quite a technical challenge, are fairly tricky, but the slow movements aren't as techinically difficult, along with the Mozart, which is, in my opinion, still the gem of the clarinet repertoire, if not one of the greatest concerti ever written for an instrument. It's not that hard technically, but to pull it off is perhaps even harder than the Weber pair.
Weber's concertino shouldn't be overlooked, either.
Hindemith's clarinet works (a sonata, a quartet and a quintet) are quite good, too. The clarinet part in the Quartet for the End of Time is notable as well.
EDIT: just remebered, Mozart's Kegelstatt trio for clarinet, piano and viola.
I saw a youtube video a while ago of someone playing 'take the power back' by rage against the machine on clarinet, it was insane! couldnt for the life of me work out how he did it, and now i cant find the damn thing! but yeah from what i saw then, thats one to learn although it doesnt quite follow the general 'flavour' of the discussion :P