Sure, there may not be that much glory in shooters (Goldeneye, Halo, Gears of War), since one might argue that they are all the same game but with different skins, but it's nice to be the hero and save the day ;-) I tend to play offline because I can't justify the investment in paying for xbox live; and when I had it for free for 3 months (came with my xbox) I ended up mostly dead in Assassin's Creed and Halo multiplayer without any sense of accomplishment - so xbox live is only there for the sports (whenever someone gives me a membership as a gift ;-) )
Other games include games on my iPad - casual games like "the end" or World of Goo (which I first played on my Mac).
If all else fails, I also have a PSP which I rarely use. I like it, I like the games...but I find the lack of achievements on the PSP unmotivating ;-)
Have you played Little Big Planet on the PSP? That's good fun. The ability to construct, customise, play and share your own little big worlds with others is a good feature! You can probably pick it up secondhand at a reasonable price! :)
I have played LBP :) Oddly enough it's not a game I would choose to buy (I don't know what my bias is) but when the Sony store had that hacker meltdown (or whatever it was) and gave away 2 free games, I opted to use one of my free game vouchers for LBP. I am so glad I did! It is a fantastic game. Granted, I haven't done much customizing (other than posting a random sticker here and there) but I do plan on checking out what others have made :)