There are about twenty-seven members of the clarinet family, many of which are obsolete in modern music. I've studied this subject the most intensely, and I've come across over thirty different types of clarinets, ranging from ten inches to over six feet tall! Here is some information about each clarinet: 
Clarinet in A Flat
This clarinet is the rarest of all the clarinets. It stands about fourteen inches tall. It is known as a Sopranino Clarient. It's used in military bands and in the continent of Australia. Leblanc makes this clarinet in the Boehm system, while Ripamonti in Italy makes it in the Muller system. It can also be made in the Deutsch system.
Clarinet in E Flat
This clarinet is a little bit larger than the A Flat clarinet, and I have the pleasure of owning one. It's rumored to be very high and squeaky, but as long as you invest in a tuner, it should be fine. This clarinet is often used for small children who are beginning to learn about clarinets at a young age. This is about seventeen inches tall. It's often used in large symphonies and clarinet choirs. This instrument has a very bright tone, and it was built to replace the trumpet or cornet in orchestras.
Clarinet in D
This clarinet has a very bright tone. It i snot very common in the United States, but in large ensembles, you may fine one. I haven't found much information on the clarinet yet, except that many large manufacturers still make it.
Clarinet in C
This clarinet was made so the aspiring clarinetist doesn't have to transpose music to B Flat. It's in the same key as flutes, bassons, pianos, and violins. It's rarely used, but Brahm and Beethoven have written pieces for this instrument. It stands a few inches shorter than the B Flat Clarinet.
Clarinet in B Flat
This is, by far, the most common clarinet. It's used in a wide variety of styles, such as symphonies, marching bands, jazz ensembles, clarinet choirs, and military bands. These clarinets are the most preferred, because they have a large range of notes, over four octaves! It takes a few years to produce a musical tone, but it has the richest voice and the widest range of dynamics.
Clarinet in A
This clarinet is rarely used outside of large orchestras, as most clarinetists use it to transpose tricky keys to this easy key. It's a few inches longer than the B Flat Clarinet. It has a full, deep, melodical sound which was used especially in the Baroque Era.
Clarinet in G
This clarinet is also known as the Turkish Clarinet. It's made in the Albert and the Oehler system. The Turkish music theory divides it's octave into 48 steps. This system is supposedly more flexible than the Boehm system.
Bassette Clarinet in A and Bassette Horn in F
These clarinets are more or less obsolete. The Bassette Horn is the same size as the E flat Alto Clarinet. It is more common than the straight Bassette Clarinet in A. These are wonderful instruments with dark tones. They're used mostly in clarinet choirs.
Alto Clarinet in E Flat
This clarinet is pitched one octave below the Soprano E Flat Clarinet. It takes a long time to get used to the larger size and methods of intonation. It's used to replace the third clarinet part in many concert bands. It sounds great with bass clarinets and clarinet ensembles.
Bass Clarinet in B Flat and A
These were believed to be invented by G. Lott in Paris in 1772 or Heinrich Grenser in Dresden in 1793. These are very useful instruments for symphonic bands, as they add a low and colorful voice ot the ensemble. Some can go down to low E Flat, but some can reach the depth of low C.
Contra Alto Clarinetin EE Flat
This clarinet is one octave below the alto clarinet and two octaves below the E Flat soprano clarinet. It is made of either metal or wood. It comes in a straight version, which is extremely tall, or the paperclip version, which has become more and more rare. I've played one of these once, and they're very difficult to get high notes out.
Contra Bass Clarinet in BB Flat
These clarinets are entering the DEEP BASS voice. These are very tall, over six feet! They're less common than the Contra Alto Clarinet. Not much is known about these clarinets.
Octo Contra Alto Clarinet in EEE Flat
This clarinet is EXTREMELY low! It's one octave lower than the Contra Alto Clarinet. Only three are in existence, and they are all owned by Mr. Leblanc (Who is very lucky ot have them!). The picture shows Mr. Leblanc playing his paperclip model of this clarinet.
Octo Contra Bass Clarinet in BBB Flat
This clarinet is the rarest of all, because there is only one in existence, owned by Mr. Leblanc. Nevertheless, some songs were written for it. There is no recording of this clarinet, but it has a range from the lowest C on piano to however high Mr. Leblanc can play.
Chalumeau
This instrument is the clarinet's ancestor. It is a simple rustic reed pipe with nine keys and a single reed. It looks similar to the recorder, and it was used in the middle ages for folk music. It was updated by Johann Christoph Denner and his son Jacob to make the clarinet. Here are a few pictures of old clarinets, and these are, by far, the weirdest:
Saxonette
This is not considered to be a true clarinet, but rather a cross between a clarinet and saxophone, although it has more in common with the clarinet. It's referred to as the French Clarinet. It's pitched in C, and it is believed to be invented in France around 1930.
These are the main members, but I've also recently hear rumors of some ancient clarinets called the Clarina, Heckelclarina, Heckelclarinette, and the Holztrompete. Fact or myth? That is for you to decide.......
Here are some more pictures of clarinets that I've come across. The pictures I put above sometimes don't come up right, so to see them, click on the links at the bottom. These aren't necessarily the ones listed above, I just thought they looked neat.
Here's a very shiny mouthpiece!
Here's a picture of the different sized barrels used on clarinets. You probably thought that since the A Clarinet was bigger than the B Flat, it'd have a bigger barrel, right? Well, surprisingly, it doesn't!
This is the straight version of a Basset Clarinet in the key of A. Cool, isn't it?
This is a regular B Flat Clarinet.
(Left) D Clarinet 
(Left) Basset Horn in F
Here's some pictures of the clarinets that might not have appeared above. These are in order from smallest and highest to biggest and lowest.
A Flat Clarinet:
E Flat Clarinet:
D Clarinet:
C Clarinet:
B Flat Clarinet:
A Clarinet:
G Clarinet:
Basset Horn:
E Flat Alto Clarinet:
B Flat Bass:
EE Flat Contra Alto Clarinet:
BB Flat Contra Bass Clarinet:
Here's a picture of the clarinet family:
I have gotten most of this information from http://hem.passagen.se/eriahl/clarinet.htm
I also got some pictures from http://lachesis.caltech.edu/jayeaston/
These are instrument ultra sites!
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