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Pick-up-and-play games
Not sure what you mean by this exactly... Games without a storyline? Or games that are easy to learn the mechanics of?
Crackdown is a game with somewhat of a story, yet its sandbox mentality makes this a pick-up-and-play game for me. It never makes me feel like I need to remember what I was doing or why.
There's not much of a learning curve in terms of controlling the character either.
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FPS
Disclaimer: I have not yet played
Bioshock or
The Orange Box. I imagine both are very worthy to be mentioned in this category.
Recommendations here depends a lot on what kind of shooter you prefer: slow or fast.
In the slow-paced category you can't go wrong with
Ghost Recon: Advanced Warfighter and its sequel. These can be played in either 1st or 3rd person. Another gem in this category is
Rainbow Six: Vegas, which is strictly 1st person.
In the faster paced category you've got
Call of Duty 2 and
Call of Duty 4 (forget about 3) which are two of the best FPS games currently available.
And if you're cool with 3rd person shooters I highly recommend
Gears of War. This is my favourite game so far this generation.
There's obviously also
Halo 3. While I prefer all of the aforementioned games to it, there's no question this is a quality game if you enjoy faster paced sci-fi 1st person shooters. The replay theater alone is worth the price of admission.
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Hack and slash (God of War type stuff)
Like Moogle says... not sure there is too much hack-and-slash stuff available on the 360... There's
Castlevania: Symphony of the Night on Live Arcade, also the original
Prince of Persia with pretty new graphics.
This is also not one of my kind of genre, so there may be something out there that I'm not aware of.
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Racing (more Burnout than Gran Turismo)
Burnout: Revenge is supposedly good, but I haven't tried it. Ditto to
Project Gotham Racing 4, which is closer to Gran Turismo than
Burnout, but it's still classified as an arcade racer and not a simulator.
Now... Up until the release of
Forza 2 I also firmly considered myself more of a
Burnout racer than a GT racer. Then my brother made me try
Forza 2 and there's something about it that just clicked. I think the ability to tweak the difficulty (in a few different ways) at any time prior to each race is the main thing. I often find myself trying to play more sim-like, without ABS breaks or steering-line (a coloured line painted on the road showing when to break and the best path) or one of the other help features. But then when that becomes too difficult, I turn on one or more of the features, and the game becomes fun.
So, if you're the least bit interested in racing, I'd at least rent
Forza 2 and take it for a spin.
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Others
This is my own category for you.
If you like stealth games, you can't go wrong with either
Splinter Cell: Double Agent or
Hitman: Blood Money.
Prior to
Splinter Cell: DA I had not played any previous SC games and from what I hear this is a different experience than the previous chapters, so if you really enjoyed those you may want to rent this first. But I really liked it.
I'm usually not big on sports games, but
Fight Night: Round 03 is great fun. Especially in 2-player mode (offline or on), but the career mode is fun too. And how can you resist creating Rocky Balboa in build-a-boxer mode for your career?
Xbox Live Arcade favourites include
Cloning Clyde,
Wik,
Eets: Chowdown and
Zuma. I've also bought a couple of traditional tabletop games like
Backgammon,
Hearts and
Texas Hold 'Em.
With Live Arcade the main thing is to just download and try whatever seems fun.
KM