The Mozart Clarinet Concerto in A is one of the finest pieces ever written for clarinet. It was written near the end of Mozart's life, in 1791, before his famous Requiem. It has three movements: Allegro, Adagio, and Rondo Allegro, and is a little over thirty minutes long.
Mozart originally wrote the Concerto for the basset clarinet--in fact, he wrote it for his friend Anton Stadler, who invented the basset clarinet--but you don't see too many of those lying around in music stores these days, so the piece is generally transposed for a Clarinet in A or a plain old B-flat Clarinet.
To me, the Clarinet Concerto is the purest example of music itself. It is completely abstract, it varies endlessly on a beautiful theme, and it radiates emotion. Also, it shows off the clarinet itself perfectly: it covers almost all of the instrument's huge range, and explores the tone and technical possibilities. The first movement is rich and dark, the second movement is mournful and deep, and the third movement is delighted and unrestrained.
I think I like the Clarinet Concerto so much because Mozart makes it seem so natural. Every note and phrase is so perfectly placed. When I first heard it I thought: "I have to learn to play this." (I play clarinet). I got a copy of the sheet music and started noodling (technical term for playing the tricky bits on a clarinet) around on it. I am still trying to get it right, but it's worth every minute of practice.