The amateur radio service has its own designated format for call signs: one or two letters, a single digit, then one to three letters. These days, the FCC normally issues a new licensee a "two by three" call sign (two-letter prefix, three-letter suffix), but depending on your license class, you can qualify for a shorter one. The Advanced and Amateur Extra license classes are allowed to have 1x2 or 2x1 call signs. According to the ARRL[1], there are currently 38093 Advanced licensees and 150793 Extra licensees (Advanced is no longer issued, but there are still quite a few Advanced who never upgraded to Extra).

Of course, a call sign can only be held by one licensee at a time, and most (or all) of the 1x2 and 2x1 are assigned (I'm not sure on the current state of things with 1x3 and 2x2). So one only becomes available when the previous holder loses it (by license expiration or death). There are far more Advanced/Extra licensees than short call signs.

There are also 1x1 call signs, but they are only issued on a temporary basis to special event stations (e.g., I have operated W8C, with a club whose normal call sign is W8YY).

1: http://www.arrl.org/fcc-license-counts