Robert, your comet theory is clearly the best explanation, I don't know how we haven't thought about it before! There is something so godly and at the same time so low about drinking (mainly wine, I'd say, and Dionysus would agree with me; though I guess I could tempt him to a glass of Vintage Port). You can do it with elegance and style, and the next minute (the one glass too much) you are making a fool of yourself or (the too many glasses too many) you are flushing your guts and your dignity down the toilet. A delicate balance, an art almost, the ability to reach exactly that level of drunkenness which suits you that particular evening.
I've seen people drink systematically and literally have two different personalities of equal importance. If you let me generalize, I'll say that the British drink in order to be able to talk about themselves (otherwise the inhibition is too strong) and communicate their feelings. And also because it is part of their culture (Withnail and I said it all). In Italy drinking is very much connected to having a good meal, bringing together two of the greatest pleasures in life. An italian proverb states that the one who doesn't drink in society is either an enemy or a spy.
So drinking makes us sociable, more tolerant of other people, more ready to see connections and to transform trivialities into amazing discoveries. It also makes us outcasts if we do not indulge: have you ever tried to be a non drinker in Bavaria? You won't have a social life, period.
Personally I like drinking, but only when I manage to reach that precise state of suspension between still knowing what's going on and allowing myself some liberties. Recently I got very drunk on the last day of a mathematical conference. I had a long conversation with a professor based only, if you'll excuse my french, on the word "fuck" and its variations. It seemed very important at that moment to stress my arguments with adjectives and adverbs from the fuck-patois. I'm sure the professor was seeing the point too. Now, this exercise may be a bit dangerous, as you can surely see, but I am convinced that there is a way of charming your audience and dragging them into your state of mind (even if they are not as drunk as you are) without them noticing too much how altered this state of mind is: as I said, it's an art, it requires the ability of controlling your loss of control, I find it challenging and very interesting.
On the other hand, as you say, why can't be as free and happy without the aid of the bottle? Isn't it a bit sad that we like it so much to live, though for just a few hours, in this parallel world of peace and love? It's a big issue for me. I don't do drugs and hate any kind of addiction, I claim to be against all big escapes from reality (not like reading a book, but more like playing computer games 20 hours a day: I've done it for some time and I was very miserable). But I still enjoy and indulge in this occasional merry escape from reality which 4 (or more) glasses of red wine provide. Is this a contradiction?
I will also add that it's not always a family thing. I come from a family of non drinkers (they're not against it, they just don't like it), I don't feel particularly rebellious, it's more a matter of taste. I'm also particularly resilient to the pressure of social persuasion. But I'll join Robert in finding that positive things can come out from  letting (moderately) go every now and then. Lechaim!

So I've been going through James' lectures on the Varieties of Religious Experience and perhaps we should give him a word here:

"Knowledge about a thing is not the thing itself. You remember what Al-Ghazzali told us in the Lecture on Mysticism, -- that to understand the causes of drunkenness, as a physician understands them, is not to be drunk. ...Knowledge about life is one thing; effective occupation of a place in life, with it dynamic currents passing through your being, is another."

Layla's lovely phrase, "so godly and at the same time so low," has also an interesting resonance with the way many of James' secular intellectual listeners seem to expect to hear religious experience described: corresponding to a kind of suppression of the rational faculty. (Obviously, there's a long and rich theoretical framework for thinking about various parallels between ecstatic mysticism and drunkenness -- this was a small remark in the opposite direction.)

My question isn't so much about why we drink because there are probably a million little reasons along with that nice big one which is that it is fun. But I want to know why we play drinking games.

This might be a phenomena of high school and college aged drinkers just learning the trades of boozing for extended periods of times. At least I hope it stops after college. I hate drinking games. I like games. Games are fun. But it's as if drinking games were invented to be as little fun as possible. They are little more than guess what card I'm holding. Or throw this little ball into a cup. How come we can't at least play games we already know are fun. Like wiffleball or trivial pursuit! Or better yet, why can't we hold a conversation in a circular format! I've always found that drinking games were the biggest buzz kills of all. Talk about irony. Or don't, I'm not forcing you to.

That little rant aside, I am now a bit curious as to what the popular drinking games are elsewhere in the world. I can't imagine a culture that doesn't have some sort of variation on drinking games. In America the most popular is Beirut (Also known as beer pong but I find the former much less embarrassing to say). And then quarters followed by a whole slough of cardgames, each one more boring then the next. Beer Pong is actually pretty a fascinating social phenomena, I'd be surprised if there aren't any academic papers on it somewhere on Google Scholar. I can't count the number of parties (and I use that term loosely) that evolved or devolved around the table where Beer Pong was in action. It's usually the indicator that I use to decide whether something is or is not a party. It can be a party if there is a beer pong game and table going, but if at any point that table is the sole point of interest for the group of people then that is not a party and I'm hopefully out the door.

The social implications go even further. The table for beer pong is kind of like the opposite walls at a middle school dance. Except instead of awkwardness and cute displays of courage, there is male insecurity and overcompensating levels of competition. It's a very uncomfortable room to be in. I wouldn't recommend it