My favourite original PS2 games off the top of my head:
Shadow of the Colossus, ICO, GT3 and 4, Forbidden Siren, Jak 1,2,3, MGS2 and 3, Silent Hill 2 and 3, Shadow of Destiny, Zone of the Enders 2, Ring of Red, FFX and 12, DMC1 and 3, Onimusha 1,2 and 3, Okami, RE Outbreak File 1 and 2, RE4, Haunting Ground, Clock Tower 3, Tekken Tag and 5, Ace Combat 4, Time Crisis 2, Persona 3 (played portable), NFS Hot Pursuit 2, GTA3, Vice City, and San Andreas.
8 of these were ported to other platforms within the same generation, one of them was ported from another console (RE4). The majority of PS2's beloved original games were exclusive, a few timed exclusives, the rest multiplatform. It's an era where the best original/new games were more often than not exclusive.
I didn't particularly enjoy many favorites like Ratchet (only played the first game), Sly (same), God of War, and missed out on or barely played countless others (Xenosaga, Shadow Hearts, most Sony JRPGs, Ape Escape, Wipeout, Everybody's Golf, Syphon Filter, SOCOM, Virtua Fighter, Nightshade, Grandia, Klonoa, Katamari, Gradius V, Maximo, PS2 Suikoden, Breath of Fire, Front Mission, Valkyrie Profile, Armoured Core, Kuon, Rule of Rose, all SMT's barring P3, Baldur's Gate DA, Tony Hawk's Pro Skater,TimeSplitters, etc).
