I don't think there's any decisive winner - but if you really forced me I'd go with Doom 3.
Doom 3 has the most impressive engine going for it. Its potential is really very special indeed, and while some of the objects do look "plastic" - with a little tweaking you can get it looking incredible.
Half Life 2 really doesn't look that great in default. It has an HDR bloom mod that is quite nice, and the engine has some nice tricks up its sleeve, but overall it just doesn't seem to quite measure up to the mark.
Far Crys lush environments and massive areas of play (while maintaining high frame rates) are really very nice, but the textures lean more towards the "comic" than the "real" which isn't to my taste entirely. Also, the player models are a bit long in the tooth now. Some of this could be down to a matter of taste though.
Halo 2 just doesn't look that special. It looks good - but it doesn't really separate itself from the pack at all. Again this could be down to a matter of taste (and I've never actually played it, I'm going on the screenshots).
I'd like to nominate a game of my own if I may. Need For Speed Underground 2 on the PC. Normally I don't play driving games for the PC and I wasn't sure I'd like this one - but I thought I'd give it a go. Having cranked the settings up - I must say I'm very pleasently suprised. It looks quite simply fantastic. If Grand Theft Auto upgrades to a similar look - it'd be a landmark game. It does look a lot better when it's moving (but these things always do). Suffice to say, it does quite a nice job.

Update:
Also, when you think about it, personal taste plays a big big part as well. Half Life 2 focuses more on decaying East European cities etc. Doom 3 is all about claustrophobic corridors of a military installation - therefore quite drab colours. Far Cry takes the prize for vast open spaces and lush vegitation.
The point is, if you hate dark and claustophobic corridors then of course Doom 3 is a bad choice. If wide open vegetation doesn't float your boat then Far Cry won't win the prize for you. So it's not necessarily down to which looks best - but to which looks best at showing off the bits you like about gaming.