Download a 64-bit game (if available) on Ubuntu 64 bits
I've recently downloaded the Penumbra series. It took me a while to figure out why it wouldn't launch.
Apparently I had to re-download all the libraries it relies on. I had them already, but not their i386 version.
It is too bad because (1) there is no error message when launching the game from steam (there's a black screen and that's it), (2) I'm pretty sure there is a 64-bit version of this game (Amnesia does have a 64-bit version - I had it from Ubuntu Software-Center). The only way to figure this out is to try to run the game directly from the command line and see the error messages, you can see the libs' name that you have to download one by one.
If the game publisher provides a 64-bit version of their program, why not propose it to Steam Linux 64-bit users?
EDIT: after having downloaded all the missing libraries, the game now crashes upon loading - no more black screen, but a segmentation fault, so it closes right after launching it. I still think it's due to some incompatibilities with the 32-bit version of the game and Ubuntu 64-bit.