[color="#9932CC"][font="Microsoft Sans Serif"]I rather like my 360; while I don't have Live or anything, I enjoy my library of games, and it's fun all around.
As for games, let's see...
[b]BlazBlue series:[/b] Fighting games are not everybody's cup of tea, but since you have MvC3 listed [which I would have also suggested], I figured I'd give it a shot. I also know you tend to play games with a more visual novel-ish slant to them [like Ace Attorney, Professor Layton, etc], which BlazBlue also has. It's a 2D fighter which, unlike a lot of fighting games, is very rich in story and plot. The story is laid out like a visual novel, with multiple endings to each character's story arc, so be prepared for clicking through a lot of dialogue [although, thankfully, they're all voiced -- with Japanese/English options, no less -- which takes the edge off it a bit]. The combat's also fun, and the games are just pretty addicting all around.
[b]Super Street Fighter IV:[/b] Quintessential fighting game series, really. Pretty fun [and frustrating...]
[b]Tales of Vesperia:[/b] I gotta give a plug for one of my favorite game series, and since Vesperia's a good entry in the series, I shall be recommending it all the same. The battle system's frentic [although kinda button mashy, but that's par the course for action RPGs], the graphics are [i]gorgeous[/i], looking like a real anime [and I am far, far from a graphics snob], and it's all around good times. It's also not a game to cut your teeth on if you've never played other games in the series. Also Yuri Lowell is like the best RPG protagonist ever and is amazing.
[b]Half Life 2:[/b] I am not a big FPS fan, either, but I found what I played of this really fun. The fact that it actually has a good story to it probably helps.
And I obviously encourage [b]Portal[/b], which you've listed. I want -- no, I NEED the second game, ugh.[/font][/color]