Time Crisis 2 I got that it was OK for 1 hour solo 30 mins 2 player
Games like that are good but only for a short time plus Time Crisis 2 is easy.

Classics I would say R-Type it was a benckmark (Although not the first of its kind)

Modern Not to sure about that
PS2 Quake 3
PC Unreal Tornament (PS2 version was poor)
PS2 Grand Theft Auto 3 with the cheat that makes everyone fight