Unconventional Clarinet Technique
The history of the clarinet has been amply described in other writeups, but it's worth noting that there are several unconventional ways to play the clarinet which still result in interesting sounds. Apparently someone named Phillip R. Rehfeldt wrote a book, New Directions for Clarinet, about this at some point, but I learned these tricks by experimenting with friends in high school band.
Rather than actually playing distinct notes, the clarinet can make a noise that starts at one pitch, and ends at another higher or lower pitch, hitting every pitch in between smoothly. It's actually possible to go from high to low and back again repeatedly, which sounds amazingly like a siren. This kind of pitch-bending is much more common on instruments like the guitar, either by bending the strings or by using a slide, but this is still a relatively common technique in jazz. The solo at the beginning of George Gershwin's Rhapsody in Blue has a great example of this. Note: it's really hard to get a smooth glissando from the low register into the high register, but it's possible. (I never managed to do it, but my friend could.)
Related to this is the fact that by controlling the embouchure, a clarinet player can play most notes on the clarinet without actually using the correct fingering. With enough practice, it's actually possible to play complete songs without changing fingerings at all. It's not so hard to do with Mary Had a Little Lamb, but I've had the privilege of hearing a rendition of The Star Spangled Banner played in this manner. Not something I'd want to inflict on other people myself (only because it's so difficult to play on pitch, not because I don't like the song...), but worth hearing if only for the novelty of it all.
There are a few different techniques for getting multiple sounds out of the clarinet at one time. Some people are apparently capable of singing or humming while playing the clarinet (although I haven't heard either of those...)
The easiest technique is something that any beginning clarinet player has actually done, although usually not on purpose. Typically, when a clarinet squeaks or squawks, what you hear is the note the player intends to play, and then a frequency that they don't intend to play. With enough practice, it's possible to do this on purpose, and even control which two pitches are simultaneously generated.
There are even some methods of playing the clarinet which involve removing the mouthpiece. For one thing, simply using using the fingerings with enough force will generate a pitch as the fingertip slaps over the hole, but a much louder tone can get generated by slapping the hole where the mouthpiece should go with the palm of the hand. That makes it a bit hard to play with both hands, though, so it greatly reduces the range.
Alternatively, it's possible to still blow air through the clarinet without a mouthpiece. Using the same sort of embouchure as when playing a trumpet or other brass instrument, the player can put his lips to the barrel of the clarinet, and play.