Professor Braxton used to play a mean B flat clarinet earlier in his career (Montreux/Berlin concerts), as did Tony Scott in the 50s & 60s. Apart from this straight model, usually just known as 'the clarinet' there's a model in A, which gives orchestral player an easier time with sharp keys, an octave below the standard B flat one, there' the bass clarinet, brought to maturity as a solo instrument, history books tell us, by Eric Dolphy. Buddy de Franco used it on one album only called 'Blues bag' with Art Blakey. Later notables on this instrument have included Rudi Mahall, Michel Portal, Louis Sclavis & Jacques di Donato. A farther octave down is the contrabass clarinet; a fit instrument to communicate with whales, some wag remarked. Braxton & German Wolfgang Fuchs are noted performers on this, as is remarkable Californian multi-instrumentalist Vinny Golia, who plays nearly every instrument with a reed in it.
Prof Braxton, surprisingly enough, plays both Bb clarinet and flute on the Merkin Hall duo with Richard Teitelbaum on electronics, recorded in 1994, long after I thought he'd more or less abandoned these instruments. (I think he decided to pull out everything he had for this gig on account of RT having such a massive range of sampled and synthetic sounds.)
And, while we're listing clarinets, there are plenty more to choose from: above the "normal" Bb model there are instruments in C, D and Eb and a sopranino in Ab, and below the Bb there's the basset horn in F and alto in Eb before you get to the bass, and then the contraalto in Eb between the bass and contrabass. And that's only the ones in current use: going back a century or two, as our resident clarinet expert Mr Sudden will tell us, there are many more different ones.