Hey everyone, I'm getting a computer that is definitely not a gaming computer, so it doesn't have great specs.  Can anyone name some games that it will be able to run?
 
here's the specs

Why did you not opt for a gaming computer to begin with?

Well, all modern 3D games aren't going to run on that... even if they can it would be a slideshow. (I should know, my GPU died so I'm stuck with an Intel Integrated Graphics card for now).
 
2D stuff like Diablo 2 or Plants vs. Zombies will run fine on it at least. 3D Stuff like Torchlight will probably run on that system.

go for popcap games there ace, 
 
and web browsing games r getting good 
 
u dont even need much to run some stuff these days  
 
java wins 
 
popcap, plants vs zombies ect 

Safe bet:
 
 http://www.gog.com/en/frontpage/

" Safe bet:   http://www.gog.com/en/frontpage/ "

Not much. Monkey Island (Whatever the remake of the original was) would work. Fallout 1 and 2 which are both still relatively awesome.  Original Half life and Counter Strike maybe?
 
Also, alot of Indie stuff should work Minecraft, Drone, Space Station 13 (which is free, just get the byond engine from the link.) but also extremely weird, but awesome

You could play a lot of games, no fps or action games, but stuff like strategies (Civ, maybe even starcraft) or adventure games should run. Also a lot of older rpgs, planescape, arcanum, etc. I'm not sure, but try dragon age too even. I think i heard someone running it on an i3 with no graphics card.

Maybe Max Payne 1 and 2?

" would it be able to do something like alien swarm? "

A good list of games that could run on your computer would be
Plants vs. Zombies 
Torchlight 
Trine 
Orange Box 
 
Those should run fairly well on your computer on around medium settings at least. 

" would it be able to do something like alien swarm? "