While some mods are basically cheats I would recommend you ones that improve gameplay experience and make game more exciting instead of giving significant advantage to player.
Community Patch - better AI (you can also install Community Balance Overhaul, but that's completetely new game).
Info Addict - detailed statistics during you game.
Global Relations - shows your trade and diplomatic opportunities (not compatible with Info Addict since it's lite version of latter).
More Luxuries - this is amazing. Adds new luxury resources to the game (generated maps remain balanced).
Faster Aircraft Animations - must have in my opinion. I used to avoid building bombers and fighters before found this awesome mod.
Cultural Diversity - adds some unique starting bonuses and soundtracks to every civilization (most of custom civs also support this mod).
Not very important, but decent as well:
Slower Research - increases science costs (there are several versions - you can choose percentage)
Appropriate General Names
Maze World map script.
Waterway Exploration map script
