EDIT: Oh my god how did I forget about One Finger Death Punch. Buy One Finger Death Punch. Unless you have extremely high blood pressure, there's no reason not to grab this cuz it's cheap and incredibly addicting and anything can run it because it's basically a flash game. I think it's exactly what you're looking for, provided you're the kind of gamer who's into leaderboards or getting perfect scores or whatever.
VetosChrom3w0lfRisk of Rain
Fantastic game, but I wouldn't recommend for bad PCs. The graphics are simple sure but it's not very well optimized; even midrange rigs can get some pretty awful lag later in the game just from the amount of enemies spawning in constantly. Rogue Legacy is a pretty good game, in the same vein as RoR but a bit more lightweight.
Yeah Risk of Rain is fun as hell but it chugs like a motherfucker on my laptop. I still played it for like 55 hours and 100%'d it even though I started getting below 30fps in the final stage. Really drained the fun out of the game which stinks because it's outrageously fun.
Anyway the recommendations in this thread have been really amazing so far but I would personally say check out Platformines. Mechanically it's like a toned down Contra, but other than that, I think I would describe is as 2D Borderlands. There's a decent-ish amount of content if you just like mindlessly collecting loot and stuff.
I also recommend Hammerwatch if you've ever played a Gauntlet game. Hammerwatch is a tremendously faithful and very well done throwback, runs smooth as butter on a calculator, and its single player campaign is a decent length. I've played for almost 10 hours and still haven't beaten it which is pretty incredible. It's not randomly generated or anything so there isn't much replay value but it's still a pretty solid game.
Other than that, yeah, roguelites/rougelike-likes are always a good buy. Binding of Isaac, Rogue Legacy, Faster than Light, Risk of Rain, etc etc. Roguelikes themselves are also a good choice. Dungeons of Dredmor is a really great entry level roguelike, nice aesthetic, not very difficult, and it's got some nice humor. Dungeon Crawl Stone Soup is one of the best roguelikes on the market right now so I'd definitely check that out if you try and enjoy Dungeons of Dreamor.
Also I'd personally recommend Torchlight 2, if you're at all into ARPGs. Imo it's the best on the market if you're a solo player. The fact alone that you can play with no online connection gives it the honor of being the best solo ARPG around atm.