No. Simple friendliness and charity. We don't need them, so we'll give them on to someone out of the kindness of our hearts. There's no reward in it whatsoever but the feeling of making someone's day, and that's no bad thing.

Yea you get $100 for every 5 games you give away. You didn't know that?

If nobody gave anything then steamgifts wouldn't exactly work now would it?

Do you have a soul or a heart?

If some charity happens to win your giveaway, it might be even tax-deductible.

'Coz it's like " you gave me a chance to win something which I did, now let me do the same for you".
It's simple. You have bought some game(s) cheap (due to discount or it came to you from some bundle, where you already got some of those games), then you give everypony else, who was late to buy for cheap, chance to win it. So do they later.
So if it's all perfect, it's just legit way to abuse Steam discounts.

why not? this site wouldn't even work if no one gave anything away...

There are two reasons for this

1.) Charity, selfishness, at some rate the giving of the gift is the aim here.

2.) By giving out gifts (generally by buying in bulk or cheaply), one can understandable end up in one of the private giveaway groups. If getting games is the goal, you can easily recieve more gifts than you give out. In theory, I've never actually seen this done.

I mainly give out since I don't like feeling like a parasite.

I don't play a ton of high-profile games, but I really like introducing people to the games that I do like.

Games like Recettear and Crayon Physics Deluxe, for example.

Sometimes I even find it more satisfying to give a game that I like to someone else than to get a game that I've wishlisted.

Since everyone has stated the obvious charity and kindness points...
A person might give away a game they feel it good but it is under the radar in order for it to get more attention. Speaking of which I think we've had a publisher or two (or at least I think they were) create a giveaway with mass copies of their games for that exact purpose.

Hey guys, you know that thing I said about not understanding how simply liking a cartoon would be annoying?
I understand now.

I do it so I can troll

Extra copies lying around, wanting to share something you love, just because you want to. Plenty of reasons.

Way too many Brony's.

I do it because every time you give, the Flying Spaghetti Monster grows a noodley appendage.

Why do people do nice things? Wouldn't this world be better if everyone was selfish and didn't do nice things for eachother?

Seriously though, if you don't know the answer to your own question then I really feel sorry for you.

There's no reward per se, you won't get anything tangible, or even virtual with it, but you will probably get a big thanks, or at least give someone a smile.

I gift games because i can

Lord knows anything FPS is better off in someone's inventory besides mine. I gave away something I won in a Steam contest, hopefully now they have an inventory system all games like that will be giftable.

For the love of gaming! \o/

Some day, in several years time, when I'm (Hopefully) uber rich, I'm going to be single, and with the oodles of cash that I have saved from not having a partner, I'm going to make a giveaway with like 1000 copies of the currently most popular game. When the time comes, most will think it's a scam (Who in their right mind would give away $50000 worth of games... ?), but I can tell you now - It's going to be AWESOME :D