Since you fairly recently purchased an Xbox 360, I would recommend a few games based upon some that you mentioned:
1. Alice: Madness Returns (3rd person action, adventure, platformer shooter with puzzles!) - about $20-30 USD
2. Bioshock (the 1st game) - Very good story driven shooter - about $10-20 USD
3. Borderlands 2 GOTY (with all DLC) - FPS Action, Shooter with RPG elements (very funny humor) - about $20-30 USD
4. Diablo III: Ultimate Evil Edition - 3rd Person Action RPG (very fun 4 player online co-op) - about $30 USD
5. Dishonored GOTY - First Person Action / Stealth game, very good story - about $20 USD
6. Dungeon Siege III - 3rd Person Action RPG (4 player online co-op) - about $10-20 USD
7. Fallout 3: GOTY - Very good First Person RPG Shooter (with stealth options) - about $20 USD
8. Kingdoms of Amular: Reckoning - Very good 3rd person Action RPG (with stealth options) - better than Fable - about $20 USD
9. L.A. Noire - Story driven 3rd person Action Shooter (similar to GTA) except you play as a 1940's Detective in LA - about $20 USD
10. Wolfenstein: The New Order - Very good FPS Story based Shooter (with some light RPG elements) - about $20-30 USD
Just to take my mind off this mess, hope you don't mind if I give a quick review of your choices?
1. Alice is a really underrated game- it has a lot of the charm of Psychonauts combined with the aesthetics of the Brothers Quay Street of Crocodiles. Don't normally like platformers but really enjoyed that one.
2. Would have probably loved this but it gave me such bad motion sickness due to menieres that I couldn't play it.
3. Yeah that's one of my favourite games right there, great design choices and humour. Borderlands is an absolute hoot- first fps I found i could play for long periods of time without getting motion sickness as well.
4. Couldn't get on with it, guess I'm just not that into that top down gameplay unless you make up for it with excellent dialogue and... wait a minute this is supposed to not be about Dragon Age isn't it...
5. Motion sickness again, same as Bioshock.
6. See 4
7. Well I just about finished Skyrim but damn, Bethesda don't make it easy for those of us who like decent acting/ dialogue in a game. Also Vats system - got hang of it, but I'd rather use my middling skills at actually shooting a target myself.
8 Really enjoyed Amalur in a, is this the old xbox? kinda way. It was more fun than Fable 1 and 3, but Fable 2? I'd take issue with that.
9 LA Noire enjoyed it but there was something missing from this, but i can't tell you what that was- oh and the serial killer subplot was crapola...
10. Wolfenstein- this was awesome, as cheesy as Iron Sky and with a real sweet spot to the gunplay- COD esque but without the "AAAAmerica, hell yeah" right wing nonsense. You can always shoot Nazis in the face without feeling a pang of moral turpitude.
Don't know what the original list was that the original poster gave but i'd say to add to that....
In the list of criminally underrated games: Skate 2- which is amazing whether you give a stuff about skateboarding or not,
Rockstar's Bully- which is like playing an old school gta before the fun leachedd out, Dragons Dogma- I was so hoping before the new Dragon Age that they'd steal this rpg's combat- because it's the best I've played, Afro Samurai- action rpg with quite deep combat mechanics, Vanquish- Gears of War on steroids, Enslaved- again a great action rpg with platforming elements, and the Brothers in Arms series for those of you who like a good squad based shooter- which after all is what Mass Effect has at it's core.
I'd also recommend, Red Dead Redemption, the most recent Tomb Raider, all 3 Mass Effects obviously, Bullet Storm, Crackdown, Just Cause, the Force Unleashed, Destiny- even though the story is nonexistant piffle, Lost Planet- but only the first one, Gears of War, Far Cry 3 and Assasin's Creed- especially number 2- but i have got to say that's a really tired franchise now,
Would be interested to know what other favourites people have, especially on the original xbox- mine were Psychonauts, gta san andreas and the incredibly under appreciated Rogue Trooper- the game that Gears of War stole all it's best ideas from.