Best Xbox 360 games

Halo 3/4

Gears of war 1/2/3

Could list more but I'd run into Cross platform if I did.

Dead or Alive 4
Dead Rising
Forza Motorsport 4
Gears of War 2 and 3
Halo 3 ODST
Halo Reach
Ridge Racer 6
Saints Row

Unfortunately the xbox 360 is weak in the exclusive games department. Personally PS3 has better games like:

Killzone
Uncharted
Infamous
Beyond Two Souls
God of War
Heavy Rain
The Ico & Shadow of the Colossus Collection
Littlebigplanet
Metal Gear games
Motorstorm
Ratchet and Clank games
Resistance games

the entire Halo series on 360 (Halo wars - 3 - ODST - REACH - 4 )
Gears of War series
Forza Motorsport 4 and Forza Horizon
Fable 2

and if you're into arcade and indie games X360 has tons of great ones:
Shadow Complex
Dishwasher
splosion man
Charlie Murder

First of all, good luck, Xbox 360 is one of the worst console ever because it lacks exclusives, but anyway...
Gears of War 2, people really like the GoW series, I don't find it anything special but still...there's not much else on the system.
Halo series, this is by far the best exclusive you can find.
Shadow Complex, I have yet to get this one but it's one of the few you can't find elsewhere.
'Splosion Man, I have the 2nd one on PC, but the first is 360 only.
Perfect Dark, remake of the N64 classic, but still it's the only place where you can find it nowdays, same goes for both Banjo-Kazooies.

halo (all of them)
forza motorsport 4 e horizon
gears of war (all of them)

I've had a 360 for quite a while, and I strongly dislike almost all of their exclusives.

Forza Horizon is a fun mix of open-world arcade racer (ala Burnout Paradise) with some sim aspects (ala Forza).
Shadow Complex is a great game and a lot of fun.

Halo, GeoW, and the first Dead Rising are all completely skip-able.

The 360 version of RDR is supposed to be a bit better, if you didn't get around to that on PS3.

Not sure if it's an Xbox exclusive or not but I do enjoy playing Vanquish and Shadows of the Damned. I think both of these are underrated and lack exposure compared to the mainstream Xbox's games.

Halo CE (old xbox title, compatible with xbox 360)
Halo 2 (old xbox title, also compatible with 360, best game in the series gameplay-wise)
Halo 3 (pretty damn good, beware that multiplayer is near extinct, i saw like 1k players 2 months ago spread out between various game modes, hard to get matches)
Halo 3 ODST (same as halo 3)
Halo Reach (somewhat better than the previous 2)
Halo 4 (not as good as the previous 3 but still worthwhile playing)
Halo wars (different kind of Halo game, if you feel like it)
Halo CE Anniversary edition (worth it for nostalgia and it's the start of one of the best game franchises)

Gears of war 1
Gears of war 2
Gears of war 3
Gears of war judgment (have it but haven't played yet, previous 3 were pretty good from what i recall)

Forza Motorsport 2 (best racing game ever imo, sadly the multiplayer is dead, checked this 2 months ago and there was nobody online)
Forza Motorsport 3 (it's "meh", previous one was better, also FM4 is better than this)
Forza Motorsport 4 (copy + paste of FM3 from what i remember, with a bit more content and overall improved experience)
Forza Horizon (never played this but i got FH2 on xbox one and it's the funniest/friendliest racing experience ever, it's not a serious game but it's fun to mess around with)

Viva Pinata (if you like this kind of games, i enjoyed it in the early days when i got my 360)

Jet Set Radio Future (old xbox title, compatible with xbox 360, worth getting it if you like what you see)

Project Gotham Racing Series 1-4 (1-2 old xbox, 3-4 360, different kind of racing games, they provide with nice challenges if you are up for the job)

I think this is all of it, from my own experience of exclusives, i got all of them games mentioned except for forza horizon + project gotham racing 3-4. There's also Dead Rising 2, i have this but it's really not a big deal in my book mostly because of the timer within the game, limits the freedom element in the game, still provides some fun moments i guess.

EDIT: Forgot to mention import tuner challenge, if you ever played tokyo highway challenge on older systems and enjoyed what you played, then you should grab this too. Game is nice and plays like older similiar titles, but it might seem a bit too clunky for a 360 game, the collision mechanism is not really the best, still the game is fun to play.

The only reason to have Xbox is Halo (all of them)... and this is a very good reason.

Don't forget to play Alan Wake (nobody mentioned it yet :) ) ,dead rising, Gears of War(all of them)
Also,saints row is good.Xbox 360 doesnt have so many exclusives :(

I only have a few:

Lost Odyssey
Blue Dragon
Infinite Undiscovery

Was given an Xbox360 years ago and those are the only games I bought for it over the years. Most everything else is available on other consoles.

Best xbox games? just gears of war series and halo series, also kinect games. Most other games are multiplataform.

Raiden iv
Lost odyssey
Ninety-nine nights
Banjo-kazooie nuts and bolts
Chromehounds
Fable 2

Kameo: Elements of Power

Viva Pinata. No joke, I'd kill to play it and Viva Pinata TIP again.

Without a double Double Fine Happy Action Theater is the greatest 360 game. If you have little kids, that is.

Doritos Crash Course 1 & 2! (Both are free on the marketplace, I think)

Play Fable 2 it's awesome, especially in coop. I remember the days when I just played Fable 2, trying to liberate all the secrets of the game.

Fable II is an action role-playing open world video game in the Fable game series developed by Lionhead Studios and published by Microsoft Game Studios for Xbox 360. It is the sequel to Fable and Fable: The Lost Chapters, it was originally announced in 2006 and released in October 2008. A compilation of the game, and its two downloadable content packs, was released on 24 October 2009, titled the "Game of the Year" edition.

http://en.wikipedia.org/wiki/Fable_II

Note: I dislike the Fable 1 and did not play Fable 3.

I think ori and the blind forest is a good game.Although it has releasedon Pc, it still is a good game anyway.

Halo (all)
Gears of war (all)
Fable (all)

"sadly" xbox 360 lost most of its exclusives, they were later ported to other consoles or pc. It's good for pc gamers but crippled the exlusives list on the 360. :P

GTA V
Red Dead Redemption
Forza Horizon 1 & 2