Funny that you mentioned Benny Goodman, I just finished watching a video of Benny & vocalist Peggy Lee playing "Why Don't You Do Right"
Before I started playing clarinet, I was listening to Benny Goodman & Artie Shaw, especially the Shaw Clarinet Concerto. Probably some Dolphy as well.
After 2 years of study, I find myself coming back to these recordings from time to time:
Sabine Meyer - Saint-Saëns Sonata
Karl Leister - Mendelsshon, Reger, Danzi, Rossini & Neilsen sonatas
Todd Levy - Brahms clarinet sonatas
Stanley Drucker - Mozart Quintet
I had never heard of this one until a few weeks ago when we started looking for solo and ensemble music. we wanted to do a clarinet choir and our band director picked out a really cool, very fast piece for us. It's called Marriage of Figaro by Mozart, I recommend you listen to it once.
Stanley Drucker playing the Nielsen concerto (I believe hardest thing ever written for clarinet) with the NY Philharmonic 30 years ago. He Has been with the NYPO 60 years, 49 as Principal Chair and WILL retire June '09 at age 80.