Oh, how I wish thet had released Front Mission 4 in the UK.... I love Front Mission 3 on the PS1, it's an amazing game. Front Mission Evolved, however, is the sort of gaming abomination that makes me want to rinse my brain out with a solution of salt water and ground glass in an effort to forget it.

Many of the good ones have been mentioned already.

The Jak and Daxter games are great action-platformers (and Jak X is a fun combat racing game).

Transformers (not the one based on the Michael Bay movie) is a cool third-person shooter with huge, open levels and great graphics for a PS2 game.

The Baldur's Gate: Dark Alliance and the Champions of Norrath games are good if you like hack & slash style ARPGs. The Dark Alliance games were also released on the Xbox.

Mercenaries: Playground of Destruction is a fun open-world third person shooter (also released on the Xbox).

I really, really am not any kind of Sony fan but the PS2 probably has the best game line up of any console ever. No, the PS2 itself was kind of inferior to my Dreamcast, but the games... man, you are missing out if you haven't been playing those games. There's a reason the PS2 is the all time best selling console and why it still outsells the current gen of consoles.

The PS2 has some great games (a lot of bad ones too), most of the good ones are already mentioned.
For me I think the best ones are the Gran Turismo 3 and 4 because I have a weakness for racing games and these are very good.
The only reason I don't play them anymore is because since I have a high resolution flatscreen tv the games look awful, they were much better looking on a normal tv.
Too bad I can't play them on an emulator (cpu too slow, compatibility issues, etc.).

Another thing, a lot of good shmups were for Japan only, which is a real shame, if there is anything we need here it are shmups.

Seconding R&C, the Ace Combat series, and Timesplitters. Played those myself and loved them.

A lot of the good titles like the big three sony platformers, DMC, ZoE, MGS, etc. ended up getting HD remakes.

Wizardry: Tale of the Forsaken Land
Nocturne, Digital Devil Saga
Dark Cloud 2
Growlanser
Gradius 5
Castle Shikigami 2
Breath of Fire 5
Culdcept
etc.