Different sizes from E flat to Contra Bass Clarinet
When somebody talks about "the" clarinet, it is very likely the B flat clarinet is meant. These are by far the most common clarinet, but from the beginning on clarinets were built and played in different sizes and scales. In the early days of clarinets there were even more types than we have today.
In the meantime a reduced set has established itself in orchestras that is used by professional players and amateurs alike. This set is part of the modern family that is shown on the picture. All clarinets except the counter base are common in orchestras today.
You will find a description of each type on its own page:
E flat clarinet (the smallest and highest)
A / B flat (Soprano) clarinet ("normal" clarinets)
Alto clarinet in E flat and bassett horn in F
Bass clarinet (the low clarinet) in B
Contra-alto and contra bass clarinet (very low and rare)
The clarinet is a transposing instrument. In the beginning there were clarinets for nearly all scales, but today only B flat, A, and E flat remain (yes, I know there are G / C instruments). If a composer asks for a C clarinet you will have to transpose the notes for your B flat or better for your A clarinet, if you have got one.
Rarely used sizes
The instrument types above are the common ones for the classical symphonic orchestra and harmony orchestras (including marching bands and big bands) of western culture. In other cultures things look different: The traditional Turkish orchestra - which by the way plays music that is harmonically and rhythmically much more complex than that of western style - employs different clarinets, for example a clarinet in G.
One reader - Thomas Aigner - writes: "... next to that there are high-G and high A flat clarinets. They are used in vienniese folk music (called "Schrammel-Musik"). In contrast to the E flat clarinet the high-G has a very fine sound. You can have this built by Schwenk und Seggelke, were you find a description of the instrument."
Can't you replace different types with each other?
This is a common question: Isn't it possible, to play - instead of an E flat clarinet - a B flat clarinet, just an octave higher than it is written? Then you could save the money for the E flat clarinet, and it would be enough to have, say, a B flat and a bass clarinet (B flat, too) for all existing literature. You do play the same notes then, don't you?
The answer is NO - this won't work well. In a tutti part, when everybody plays fff, and just harmony is important, it may be difficult for the audience to notice that you used a different instrument. When you have a more prominent part, the difference becomes more obvious: The clarinet's sound differs strongly in the upper and lower register of the instrument. Notes that an E flat clarinet plays in the sonore lower register with strong low overtones would be played in the rather neutral part of the upper register of an A or B flat clarinet. The clarinet is not a cheap synthesizer where every note sounds the same, just at a different frequency. If the composer wanted this effect, and the audience expects it, you better come close to what is expected. In case of emergency you may play a part with another clarinet of similar size (replace A with B flat or bassett horn with alto clarinet, but then you will have a transposition problem with lots of sharps or flats. So if you have to replace one clarinet with another, keep in mind that it will sound differently. Of course it still is better to play the E flat clarinet's part with a B flat clarinet than with a flute.