[Jack Simth]

Depends a bit on the specific copy-protection mechanisim involved, but yes, they can be possible.

Unless it's been coded in somewhere, the program doesn't know exactly what key it's looking for - if it did, then (for someone with enough knoweledge on the specific copy-protection mechanisim) it would be a fairly simple exercise to write something that could either alter the program to accept given key or read the key straight from the program. What's more commonly done, however, is to tell the program what a good key looks like, and then have the program compare keys every now and again against some list - other programs in the game group (for the ones where you can host your own server), those linked to the main servers (most MMORPG's), or a quiet call-home server that's not so commonly known. The comparison is usually to weed out known abused keys (those that have been used way too much - known to be compromised) and to find new keys that are being abused (e.g., three computers with the same key on at once is a pretty good indicator that something's not as desired).

A key generator, if successful, basically reverse-engineers the knoweledge of what a good key "looks like" to create keys that will look good to the program... which can also be unique (and thus not raise the alarm at the main or call-home servers).

Of course, anytime you download a key generator, you are knowingly trying out a program from an annonymous source that is already thought to compromise programs, and running it on your machine.....