(No. "Thor" is not my Game Center nickname.)
Game Center is Apple's take on a "social gaming network." It keeps track of most all of the games I play on any iOS device (iPhone, iPad or iPod Touch), showing me my high scores and giving me achievements for different in-game challenges I've completed. On some games it will connect me with someone else (a friend or otherwise) so that I can play with them. It will also compare my scores to players all over the world, including my Game Center friends.
Wait. Game Center friends?
That's my problem.
The way you find Game Center friends is so onerous, it's almost not worth using Game Center at all. In order to become a "friend" on Game Center, you need to send an email to that person using the Game Center "Add Friends" interface. And not just any email, but the email address they have tied to their iTunes account and therefore their Game Center Account (unless they've gone into their Game Center account page and associated another email address with their account - which I'm guessing I'm one of a handful of nerds who've actually done this). Then they have to see the request in Game Center and accept.
What there isn't is any kind of "Find a Friend" functionality. It seems like on every website, web service and everything else I sign up for on the Internet there's an easy way for me to find other friends who are using the same thing. Apple has the email addresses of all the Game Center people. They make the phone so I know they can get their hooks into my Address Book to see if I know anyone who might already be on Game Center. At that point they could make me send my friends an email - no problem. But instead I've got to think of my friends who may have an iPhone, and then guess the email address they use with Game Center, and then hope that they notice on their iPhone that they have a friend request. See what I mean? Onerous.
I want to like Game Center. Actually, I really want to like Game Center. Achievements are great. Seeing all the games you play in one place is great. But the real fun of having a "social gaming network" is playing with friends and then comparing (and sometimes trash-talking) afterwards. When you can't find your friends, there goes the "social" in the "social gaming network."
(Oh. And I'm not even going to get into the skeuomorphic green felt and dark brown "wood" design of the thing which is typical of much of Apple's iOS visual design ("Notes" anyone?). Personally think it looks terrible, and I'll dare to dream that someday they can think of something that looks cooler than Windows Solitaire.)
But hey, there's always hoping they'll update it in the future. I mean, we got copy and paste eventually right?
Game Center is automatically installed on any iOS 4 device.