I'm looking to buy/play:
Bayonetta
in the near future.
Do it. Bayonetta is my favourite game of the last five years. Aside from the bizarre Japanese humour and eye-melting graphics, it is enormous fun to play and one of those games that you keep getting better at and hence wring increasing satisfaction from. So deep, too - each new weapon you unlock allows you to completely change your playing style and destroy enemies in new flamboyant ways. I've completed it 5 times now and still go back to it because it's such a joy to play. I know a few people who didn't get on with it but if you've ever enjoyed Streets of Rage or Devil May Cry then you need Bayonetta in your life. (Also, if you're a fan of buttocks then this is probably the pinnacle of computer-generated arse, which the camera is worryingly eager to show you. Those Japanese, eh?)
As for other 360 games, annoyingly the vast majority seem to be realistic first-person shooters or driving games, neither of which I care for. Other things I'd recommend, though:
Fable 2 and 3 - These are a bit too easy and there are glaring flaws in each, but they manage to be hugely endearing and hide all the dull stats-based grind of the RPG in the background. Uniquely British, with some excellent humour and voice acting.
Portal 2 - This has been eulogised upthread, and rightly so, it's excellent.
Crackdown - I loved this. As with the GTA games, following the story and doing the missions isn't really the point - jumping over buildings from a standing start and throwing lorries off bridges onto pedestrians is where the fun is, a city you can create amusing chaos in.
Prototype - You can run up the side of buildings like Billy Whizz. Terrible hackneyed plot but entertainingly OTT action, and you can jump off buildings and land on people's heads.
Red Dead Redemption - Grand Theft Cowboy. I know lots of people found it a bit long and dull, but I loved it, the hero is actually someone you root for rather than a swaggering prick (e.g. Gears of War, Saints Row) and the evocation of 1900's America is fantastic. Skinning animals and picking flowers got a bit boring, but hunting bears was wicked, as were all the side-missions for the agreeably strange cast of loonies.
Dead Space - This is basically 'Aliens - the game' and genuinely terrifying in an "Aargh! i've only got two bullets and there's something coming out of that vent and fuck me it's coming after meeeeee!" kind of way. Running around in a blind panic has never been so much fun.
The Orange Box - Half-Life 2 is still brilliant, and this also includes Portal 1.
From Dust - You'll have to download this from Xbox Live but it is stunningly beautiful and soothing to play. Fill rivers with sand or set fire to forests to allow your tribe of people to cross a continent. A modern 'god game', and my new favourite thing.
Get Bayonetta first, though.