A great Xbox 360 game with an interesting plot and long campaign is Borderlands. Here's a little bit about the game:
What type of game is Borderlands?
Borderlands is a first person shooter that takes elements of role playing games.
Basically, you pick a character - soldier, hunter, siren, or berserker - and complete tasks within a huge free roaming world. You have to shoot enemies, collect loot, find awesome weapons, and ultimately it's a lot of fun.
What is Borderlands about?
Borderlands is set on a planet called Pandora, which was colonised by earth in 5252, in a search for alien resources. After the discovery that there's not actually much to be found on Pandora, the colonists leave, but release convicts that they were using a labourers.
The criminals and remaining colonists discover two things. Firstly, there's a really awesome looking vault that may be filled with alien technology and riches. Secondly, that Pandora is actually filled with horrific looking, hostile creatures.
It's your job to try to find and access the vault, but you're a little cautious as those who discovered the vault were wiped out, and nothing was left of them other than some short radio transmissions.
There have been a fair few extra missions released for Borderlands, and they should keep you entertained for a pretty long time.
Here's a video showing some Borderlands' gameplay: