If you want a J-RPG, Lost Odyssey or Blue Dragon might be up your alley. Personally I thought they were both kinda lame, but might be worth a try if you're hankering for some JRPG. Or wait a couple weeks and get FFXIII.
For more western types: Oblivion and Fallout 3 are both solid, I prefer Fallout 3, though. Also, Fable 2 is pretty good.
Also, you said no bioware, but screw that, Mass Effect 2 is one of the best games for the system. Has great 3rd person shooting action on par with Gears of War, but with dialogue and character development beyond anything else out there. Dangerously addicting. The first Mass Effect is solid for the backstory and characters, but the gameplay is lacking hugely in comparison.
Honestly, it is my favorite game on the console, hands-down. It is a freaking Final Fantasy in everything but name, but has a much darker tone than most FFs have. It's brilliant, in my opinion. It is also one of a small handful of games that everyone I work with played - since we all have very varied tastes in games, that is a big deal.
Dragon Age is worth playing but I'm assuming you've played it already since you said "no Bioware".
Fable II is worth playing. It's very quick, though. I got halfway through the story in about 6-7 hours of play. For just plain messing around, though, it's hilariously fun and entertaining. I think I had a husband in one town, a wife in another, and a girlfriend in a third. Awesome.
Oblivion bored the hell out of me, I got through about three hours of play and never touched it again.
Blue Dragon is pretty good. Not perfect, but still a decent game. I don't think I ever finished it though, because I got Lost Odyssey. I've heard good things about Eternal Sonata but I never picked it up myself. Same with Tales of Vesperia and Star Ocean.
Definitely avoid Infinite Undiscovery and Last Remnant, though. Tried them out, they're no good.
I thought Lost Odyssey had terrible character design - hated how the characters looked. And I thought the storyline wasn't as immediate as necessary. Just didn't grip me like FF games usually do.
Gender: Male Location: Living my life, fighting my war.
For a JRPG, I'd say Lost Odyssey, or just hold off for a little bit and pick up FFXIII. And Star Ocean is pretty good too, I haven't gotten far myself, but that's just because I am not in the mood to play any RPGs right now...
Western RPGs I'd say Oblivion or Fallout, both are great games if you like a good story, and a massive amount of side questing and exploration. Other than that I would say anything Bioware, but since you have already played all of them... well... I still say play them again.
Lost Odyssey - the only real JRPG I've played inr ecent times beyond Pokémon.
Fallout 3 - Really cool setting and great over-all story as well as countless great smaller stories.
Oblivion - imo a tamer version of Fallout 3 (Yes I know it came out first) with swords, still decent though.
Fable 2 - just completed it two days ago, I enjoyed it, but ti definitley has its flaws. Download the first part for free on Xbox Live under "Episodic Gaming" and see for yourself.
You get to play as an awesome vampire with awesome powers. Wanna make peoples blood boil? Check. Wanna make poeple claw their own faces off? Check. Wanna talk people into killing their own friends and family. Check.
Great characters, great plot, great backstory, great setting and a surprise ending, I doubly recommend it.
It allows you more control over your character than any other RPG in the history of RPGs! It allows you total freedom of choice over what your character does with her time; you can choose to engage in activities, go to the casino, go shopping, interact with NPCs, explore the island; the possibilities are endless! It has a very deep character interaction system, based around how much time you spend with your party, how successful you are at the different group activities there are on offer around the island, how often you send them gifts, knowing exactly which gifts to send etc.. Members of your party can also choose to leave if they're unhappy with the arrangement which I believe is pretty unprecedented for an RPG. You have to really earn the presence of your party members. New game plus feature, a huge selection of characters to play as, one of the best licensed soundtracks in videogaming, great artistic design, and a truly gripping story with a prevalent theme of greed and corruption make this game one of the best RPG experiences the 360 has to offer.