Games can be written in literally anything—if that's your primary interest, you might want to look into Lua and Love2D, or Python and pygame (as has already been suggested). Both Lua and Python are good beginner's languages—Lua because it's small but versatile, Python because it's popular for that purpose and has good tutorials.

C# . . . isn't a bad language, but it's a bit bloated, so I wouldn't choose it for a beginner—save it for when you're proficient and looking for a second or third language. Other languages I would not start with would include Javascript and PHP (because both have hidden inconsistencies that can trip you up), Perl (I love it, but it looks like line noise half the time), and C and C++ (manual memory management, which makes a lot more work for you with no real benefits unless you're writing an OS kernel or something).

What you need to do is learn to think like a programmer, regardless of language. Anyone who's been programming for ten years or so will have gone through several languages as their needs change.