I have seen transistors with the middle pin cut used in computer equipment. What do they do?
Because it isn't required. On most of those parts the middle pin is internally connected to the heatsink tab, and that one is soldered anyway, for cooling reasons. BTW, the pin isn't cut, the short tab is the way the part is supplied.
Note that the PCB can accommodate both parts with or without the pin.
They're called D2PAK or TO-263 packages (DPAK = TO-252 is similar but smaller), and they're designed that way on purpose.
As stevenvh states, the middle pin of the leadframe is internally connected to the heatsink tab -- it's actually one piece of metal! (Sometime try dissolving away / removing the packaging compound and you'll see this.)
The reason the middle pin is short is to allow for increased creepage and clearance distance. Some of the transistors in TO-263 packages are rated at several hundred volts, and getting the middle pin out of the way is a huge deal because the other two pins are relatively close to each other in voltage, whereas the middle pin is the drain/source pin which is often at a very different voltage.
Why they have the middle pin stick out at all is a little strange to me (it's still an unwanted voltage near the other two pins, and it would seem like if they didn't make it stick out of the package at all, there would be even better creepage/clearance distances) -- although I'll admit it seems just right, as you can hook a probe clip on it if you need to.
History. (As in: Why, after all, is the middle pin still there, in its strange, stub-like nature?)
The Evolution goes like this: TO-220, TO-262, TO-263
(Source: Infineon; via http://www.powerblog.de/2011/12/06/bleifreie-mosfets-in-standard-to-gehausen-fur-die-automobilindustrie/, hopefully o.k. as per fair use.)
TO-220 has been the classic THT power package for, like, forever.
TO-262 is shorter and may be handy in height-restricted mounting space. The smaller tab is not a big drawback when no heat sink is required or when you use a clamp instead of a screw to mount the part onto a heat sink. Clamping is a better choice for a number of reasons, anyway.
TO-263 could be called the surface-mount version of these THT parts. The tab and the middle pin are connected, and the tab offers a path with less inductance compared to the middle pin. With no solder pad for the middle pin, board space may be saved (other components may go where the pad would be), and insulation distance may be increased (good for high voltage parts).
Note that the plastic molding of all three cases is exactly the same. Thus, much of the same machinery can be used in the packing process of the parts, it's likely just a different lead frame.