I break the AIs down into four categories (or tiers if you like)
1) Reliable PITA: AIs in this category are serious contenders to win the game; direct intervention will likely be necessary to stop them from running away with the game. A couple examples would be Greece for diplomatic victories and Korea for science victories.
2) Frequent Nuisance: Not usually in contention to win, but can certainly make you lose and mess with your game plan. Flipping all your cities to their religion, or attacking early and often will land a civ in this category for me. I find the warmongers force more units out early, but probably won't warrant a late-game desperation attack to stop them. Examples: Montezuma, Ethiopia, Shaka
3) Nuisance: Don't necessitate a change in game plan, but can mess with yours. Maybe they'll snipe a Wonder you wanted, or denounce you at an inconvenient time, but you don't really have to DO anything about them. Best example: India.
4) Nonfactor: You might not ever meet these civs, because they're dead before you get to that continent. Even if they survive, they seldom accomplish anything and can be pretty much ignored. Examples: Brazil, Venice.
TL;DR: Four categories. "Man, I've gotta do something about that guy before he wins!", "Aw hell, Monty next door.", "Shut up, Gandhi.", "Oh hey, Venice was in this game?"