Baten Kaitos is a brilliant RPG, being quite underrated and actually trying to be a bit different in terms of gameplay and art style.
Zelda: Twilight Princess OR Zelda: Wind Waker are both excellent adventure games, but then again I do love Zelda games. Also, speaking as a foreigner, I think this might be the first time in years I've managed to spell EXZSCHELLENT in several years.
Lost Kingdoms is another good RPG game, if a bit short. It's a ton of fun "collecting" monsters and finding new weapons/cards (this was back in the day when using cards instead of actual weapons was more popular than what ever would have happened if Call of Duty and Halo had a baby together), and even though fans of the "series" -for there are indeed only two of them- have bashed the 2nd game for taking some of the more crappy parts of the gameplay and actually improved them, I still hold the 2nd game up as the superior. Maybe that is because I played that one first, but who knows.
Gotcha Force is quite an odd title, being somewhere between mech-action, cartoony spectacle fighter and Metal Arms, and it has become quite the cult classic over the years with several very dedicated fans. The game is quite rare though, so good luck finding one that's at least affordable.
Skies of Arcadia: Legends, another RPG, and a really damn good one. It was actually a remake of an old Dreamcast game which I never played. When you're not exploring dungeons, various towns and such, you're flying around a huge world with tons of hidden stuff to find. I've put over 100 hours into it, and it's still fun. Also, it all takes place in a world in the skies, because regular ground is dreadfully boring. But really, it is awesome.
Eternal Darkness has already been recommended, but allow me to recommend it some more: It's an awesome Lovecraft-inspired horror game with a good story. That's pretty much all I've got. Oh, and you can play as many different characters, which is good fun. I haven't played it in a while, mainly because I got angry at it after dying, then discovering that the game didn't have an auto save-function and having to do two long chapters all over again.
Resident Evil 4, or 4 Resident Evil as it says on the boxart. Well, it isn't really survival-horror anymore, but it's still one of the greatest action games ever made, mainly due to fun gameplay, some very intense battles and a ton of weapons, items and upgrades. Oh, and it has an infinite RPG, Tommygun and Magnum, and they all speak for themselves... very loudly.
Paper Mario: The Thousand-Year Door. A Mario RPG. What more could you ask for? Other than being an incredibly creative game, it also offers a ton of various stuff to do, some very neat characters, a surprisingly interesting story (for a Mario game anyway), and some hilarious visual humour.
Note: Princess Peach DOESN'T get kidnapped by Bowser this time. If that doesn't make you interested, I don't know what will.
Harry Potter and the Chamber of Secrets. Yes, I am indeed putting a movie-licenced game on the list, and there is a reason for it: It is actually quite good. I can't really explain why; it just has a certain kind of charm to it that I haven't seen in other movie-licenced games.
Also, it has some very amusing glitches from time to time, as well as some not-so-amusing ones.