really, between red dead redemption and gtaIV, get red dead. It's the same sort of game in more or less the same engine, but you're an outlaw in the wild west looking for salvation rather than some eastern european dude who turns into a sociopath in new york. I found red dead redemption to be a much more compelling game, and they'll both suck the time away from you.
some games I remember having fun with:
Prince of Persia (the 2008 reboot with the crazy storybook art style) - 3rd person action, I friggin love this game. People can give it shit for the "never die" mechanic, but the art style and the smoothness of the platforming stuff was done so well, I had a blast.
Batman Arkham Asylum - 3rd person action, probably the game where I felt like I was able to kick the most ass since ninja gaiden, but this game has more style, and you're batman.
Splinter Cell: Conviction - 3rd person stealth action, much more heavy on the action than the stealth, think more "bourne identity" than "mission impossible"
Halo: Reach - If you like space marines and 1st person games, this game won't dissapoint
Red Dead Redemption - 3rd person action, open world wild west, tons of stuff to do
Assassin's Creed I & II - 3rd person action, fun parkour/assassination mechanics
Mirror's Edge (you may want to rent this one first, as it's not for everyone)-1st person... parkour? It can get frustrating because you have to be pretty precise, and the 1st person perspective is limiting considering you can only look where you're running, but when you do a section right, you feel like a total badass
Gears of War 1 & 2 - 3rd person action, if you like chopping monsters in half with a gigantic assault rifle that has a chainsaw fitted onto it, this game might be for you.
Mass Effect 1 & 2 - 3rd person action RPG, If you thought halo didn't have enough story, armor permutations, or blue aliens to have sex with, you'd probably like Mass Effect. In all seriousness, they're super fun games, highly recommended.
Dead Rising 2 - Smash up slow zombies in las vegas. Need I say more? I won't recommend Dead Rising 1 because it's more or less the same game.
Left 4 Dead 1 & 2
The Orange Box (It's, like, 5 games in one for 20 bucks. And it's Valve. Nothing's better than that.)
The FEAR games (Ohgod that shit scares me senseless I swear)
The Scott Pilgrim game (It costs about 800 Microsoft points, but it's FUN AS FUCK.)
I don't like GTA at all (sorry, I can't run over people and take their money. It's not my style.) but according to my brother, it's 'beast'. Whatever that means. You chilluns scare me. (But if you get L4D or L4D2, you can play with ME. HOW GREAT IS THAT?!)
Every game everyone has listed will be fun for a time, but you'll soon grow bored of it. A 360 for me was talked up by my friends. By the time I got it I'd spent eleven days on Mass Effect, and felt betrayed by my friends.
So if you're a serious gamer, have at it. Otherwise, forking over $60 for something that'll entertain you for a brief period of time can get expensive.
On the rebound, I found that after trading in Saints Row 2, almost a year later I was feeling it again. Luckily my roommate brought it to college. Same goes for ?Oblivion, although I borrowed that from a friend and he wanted it back.
Borderlands GOTY. (All 4 DLC's come with it)
Dragon Age: Orgins: ultimate edition (again, all DLC's made for it come with it)
Mass Effect 1 and 2 (NO DLC's come with them, but their never crucial to the main plot.)
Limbo from Xbox Live Arcade. (just in time for halloween)
The newest Forza game (Xbox's Gran Turismo)
Bad company 2 (If you want a well designed/intense/fun FPS, get this game. If not, do Halo or Modern Warfare.)
I would say get Fallout 3 and Fallout new vegas. But I know they are poor compared to their PC counterparts.. same goes for borderlands. But theres really no reason to mod borderlands unless you want to cheat in which you might as well not play borderlands at all. In fallout games however, people mod them to make better bases/homes, new quests, items, etc.
Leonard, I'd actually argue that cost per hour of entertainment, video games are pretty cheap. A movie will run ya 10 bucks for a flat 2 hours of entertainment, if you get a game you really enjoy you can pay 60 bucks once and get 50+ hours of entertainment out of it. If you're on a tight budget, rent games instead and buy after you've tried it for awhile. If you have friends with 360s you can also trade between friends and co-ordinate who buys what game, then trade off so you have a larger combined libary