I've enjoyed a lot of highly-rated games on the PS2, either playing them myself or spending a lot of time watching them being played. Some of the really good games are installments of various series: God of War, Ratchet & Clank, Final Fantasy X, Resident Evil 4, etc. But if you are looking for something a little less mainstream, then I have two particular games I would recommend.
Katamari Damacy is an innovative game. While the graphics may not look like much (and the reason why I originally intended to skip this title), the gameplay is simple and addicting. Visually and conceptually it is like something thought up on an acid trip: you- as a tiny little alien Prince- have to roll a big lumpy ball around collecting various items. Simple, if strange, premise but surprisingly entertaining. The scope of items you collect range from itty bitty paperclips and ants to clouds and continents.
My favorite RPG pretty much slipped under the radar. Beyond Good and Evil by UbiSoft is awesome. It takes place in a unique universe and has a novel plot; not recycled like the Final Fantasy collection. I can't recall being bored with extended cutscenes or wearing out my thumb skipping through boring text (like many JRPGs). There's fighting, but there is also espionage, boat racing, and wildlife photography.