Wow, I'm surprised to see this kind of thread on the internet, although I probably shouldn't be considering this is Bay12.
I usually try to be nice to people around me whenever I can, even try to be always helpful and nice to people in your work-place seems to be not a standard thing. You know there's a big difference between people that, when you ask them something they just shrug and say go ask that guy instead, and the people that take the time to make sure that you got what you wanted or found the answer you needed or whatever. But some people are just dicks and will take out all their stress and frustation on you, even at work.
But then other things like giving what change or small bills you have to a homeless man on the street, offering a ride to someone that was running after a bus and didn't catch it, just being kind to people and offering help whenever you can... I'm sure all that doesn't really add up to anything in the long run and I probably look like an idiot whenever I do that. My gf certainly doesn't like it when I empty out my coins into a begger's cup, but I don't really care what the others think because I know even if it doesn't make a difference on the big scale it still makes a big difference on the individual level, even if only for just one day.
Anyway I think this thread is an awesome idea and I hope it makes a difference for someone. I don't know how you have such a huge collection of games you can give away. Is it possible to trade away games that you've already played on Steam or gamersgate and such? I do have a pretty big collection of games (around 90% of which I don't even play any more), but probably there's no way to give them away, right?
However I can offer to buy new ones as gifts. I'm not a rich man to give out $60 titles left and right, but I can offer a few people who ask any game from gog.com up to $15 or any other giftable game up to the same price. I could recommend some indie titles like FTL and Flotilla. Rogue Legacy is another one that comes to mind.
Anyway I'm doing this because I think the OP's idea is really great and I hope his goals work out (that people recieving these gifts will go and do something kind in return), so if you get the game from me you have to promise to do something nice and kind like the OP wants! (or maybe I should just send some gift codes for the OP to give out, but I don't know what game people would want...)