What sort of games can Galaxy GeForce 8400 GS Video Card - 512MB run?

Not sure about that card but the first video card i ran TF2 on was a Nivida Geforce 6600 then a 8800 that i would just buy and return before 30 days until i had money saved up for my 9800GT that i use now.

Should be ok with a 8400, though i do know that Nvidia cards run by the 2nd number not the first so you might be trying a 4 series card on a newer game, check if it runs Direct X 9 or 10.

If you have a $100 ish budget, get an ATI HD4830. If your budget is lower, try to get at least a nVidia card with a 2nd number that it greater than 6. An 8600, 8800, 9600, or 9800 is Much mch better. Also, GS cards are underclocked. Make sure you get a GT.

IF you really want to know what games any system will play .
http://www.systemrequirementslab.com/referrer/srtest
Install the file it is 100% safe i use it loads .

Here are my two recommendations, a good card, and an okay card.
HD 4830 $79.99
and
9600 GSO $54.99

Both should run most modern games pretty well, but the 4830 is definitely the better of the two.