If you enjoyed Mass Effect, maybe you will enjoy Star Wars: Knights of the Old Republic, 1 and 2. They were both made by Bioware, have similar styles to Mass Effect and are considerd by many to be some of the best games. Though they are a bit older and only on PC and the original Xbox, you can get a download to your 360 consoel that alowes you to play a range Star Wars games Including these, they still stand up pretty well.
I might also recomend Oblivion and Fallout 3, both are made by Bethseda and quite highly praised for their huge area and detail aswell as gameplay. Fable 2 is also pretty good, also has choices of morality and strategy other then combat. The Darkness is often overlooked, it is mainly FPS, but unlike other FPS you are the horror and gain power from slinking around in the dark and pierce enemies with tenticles. And lastly if you are a fan of Star Wars Star Wars: the force unleashed, is quite fun.
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Through dream I travel, at lantern's call
To consume the flames of a kingdom's fall