I own a NES, SNES, Genesis, Sega CD, N64, PSX, Saturn, Dreamcast, Gamecube, PS2, XBox, Gameboy, Gameboy Micro, DS, and a PSP.  The Saturn and the PSX are modded, the PSP has custom firmware, and I have a supercard for the DS. 

I have over three hundred games for those systems (legit and burned, but not including roms) though maladroithim is right, I guess I clearly don't like video games!

yeah but how many of those games did you actually like/play? I mean pretty much every game before the PS2 was fairly linear, and you said you don't like linear games, and you said you don't like sandbox games, and there's a HUGE CACHE of genres you said you don't like, it sounds like you don't really like games all that much and are more into casual gamer market, which there's nothing wrong with (I play mostly casual games), but then people suggest more casual games and you're like "No I don't want to play a casual game on the console" I don't really get what you want.

Unreal Tournament 3 is a great game for the 360. However, if you want fancy modding and customization then the ps3 and pc versions are the best bet. Sigh.....stupid microsoft and their "no modding allowed" law ​ 
Edit: Oh, I see you don't like FPS games.... oh well :/

I don't know if anyone has mentioned this yet, but in addition to what everyone else has mentioned, pick up Fable II when it is released. The first one was good, albeit too short and small, but the second in the series seems to improve a lot on the original's shortcomings. You said you don't really like console RPGs anymore, but you did mention Mass Effect, since it certainly isn't a JRPG. Fable II isn't a JRPG either, and I can't say it is great since it hasn't been released, but it's certainly worth a look!

If you haven't checked it out already, you might wanna check out Lost Planet for the xbox 360. The only reason why I thought I'd recommend it is because I hate first person shooters, I absolutely loath them, but for what it was, being a third person shooter, I really liked the Syphon Filter series, even if the only reason was to use that EMP Tazer and watch all your victims burn to a slow fiery death.

In the case of Lost Planet, they seem to toss in enough variety in order to keep things interesting; you fight snow pirates as well as these monsters called the akrid  and you get to jump into these mech suits from time to time and each level ends with a crazy/frustrating boss fight. But overall It progresses in the same linear fashion as Syphon Filter did but with fewer check points.

One thing I thought that was neat about the game is if you toss a grenade and if you're good enough, you can shoot it immediately afterwards and it'll make this splash effect.

Not a lot of people like this game, so this might be right up your alley, who knows.

man i just wonder like... what made them think it was a good idea to throw THE FUTURE into that?  it would've been an ACCEPTABLE story had they just left it in the past, but it really stops making sense once you make him a guy in the future with DNA MEMORY.  seriously it is so bad as to almost be funny, which makes me hope that maybe it was all a joke even though i know it wasn't.  but yeah AC is very very fun for like the first 3 missions and then progressively less and less interesting for the next 6 or 7.

spoiler alert!

You know I mentioned Fable II, I want to say that it's a shame that it is exclusive to the Xbox 360. I'd really love to play it on the PC.