I know you can view leaderboards and achievements for game your friends have played or the ones that GC "suggests" to you, but what about a game that doesn't fall into either of those camps?
Nope, not that I know of! You can always search for the game's achievements online. This is what I do when I want to know what kind of achievements the game has. As far as leaderboards, there are some third party websites dedicated to making online leaderboards.
I sometimes which Apple would just create a Gamecenter website so you can check your Gamecenter data. I think all the data should be on their servers anyways. They already have an iCloud website where you can manage some things.. Its not that important to me though..just a nice to have thing.