I actually don't know too well how half-life 2 exactly works, as i don't have the game, but i  imagine it must be something like how MMORPGs work, where u input a serial to activate the (steam) account/game. But i may be wrong.

Anyways, a keygen is impossible for online stuff because keygens are made by reverse engineering the cd key checking algorith in the game installer/exe. And since that check is done online, u cannot access the algorithm, thus cannot reverse engineer it.

Half-life 2's exe has been cracked though to completely remove the need to use steam, thus u can play it at home without the net, but u can't get updates and stuff.