Okami: Beautiful, fun, very long, plenty of replay value for collectibles (or because you forget many parts of it... seriously, long game)
Hitman Blood Money: Wonderful level design, many many ways to complete the levels, fun sneaky gameplay, weapon upgrades and customization (a favorite feature of mine in any game)
Resident Evil 4: Scary at first (then scary again on hard because you're afraid of dying), good level + enemy design, weapon upgrades and customization, good replay value
Metal Gear Solid 3 (preferably Subsistence): Awesome boss battles, great replay value, plenty of different ways to play
Devil May Cry 3 (preferably Special Edition): Really fun combat, fun weapons, fun cutscenes, good replay value (yes, I really love replaying games)
-Edited to add reasons