- Grand Theft Auto: San Andreas.
Arguably the best GTA to date. I still see GTA SA VS GTA 4 topics on occasion.
- Timesplitters: Future Perfect.
Quite a fun little shooter and the best TS to date.
- Killzone.
The original to the series.
- Cold Winder.
I found this a pretty fun little shooter to, and it seems to get overlooked a lot.
Racing?
There are a ton other shooters on PS2 like SOCOM, Medal Of Honor, Call Of Duty, etc. However there in no shortage of racing. Burnout 3: Takedown, Burnout: Revenge, Burnout: Deliminator. Most of the Need For Speed games all the way up to Pro Street. The Flat Out series, Twisted Metal: Black, etc.
PS2 is one of those consoles where there is almost to much stuff to list. It has a crap ton of games in virtually every genre.