Well I played so far Uplink and Onlink - find them really good (propably best, but can't really tell bacause I haven't tried all the games out there, but I would put a guess due to popularity), especially Onlink adding so much to the original Uplink and trying to get rid of its enoyances.
I also played Hacker Evolution and started its successor. They are OK for diverting fun, I guess.
Most recently I got to know about Street Hacker (a few days ago through this very forum here). So far it's interestingly different in the ways that it doesn't play in a future setting but rather in the present and the realism. It tries to be realistic in the ways of procedures how one would hack (not necessarily with the text commands ...). The used OS is called "Fedora"

. The enoying part here is that you can't change the resolution above 800x600. Miah, Tycho, if you find a way on howto, please let me know.
And even more anoying is the fact, that I can't start it anymore lately due to some error occurring with .Net framework and jit-debugger.
Haven't tried any others and am reluctant towards online browser games since o-game, monstersgames and pirate wars.
EDIT: I will try Endgame:Singularity next bacause so many people are mentioning it.
EDIT2: OK, I just played it trough. Nice thing. I can't wait till we get the technique of Quantum Computing for real

It was a bit hard to get startet till one has figuered out how to proceed. Safe early, safe often. But I managed to get through in 322 days (easiest mode though - and then normal mode, not much difference). Not much motivation for replay and Miah is right, the ending is a bit ... dull.
The game doesn't have much to do with hacking either.