Conceptual Balance Mod (CBM) addresses balance related concerns that many long time competitive players have with the base version of the game. This is almost certainly the most popular mod used in multiplayer games. There are a few alternate versions of this mod using it as a base as well, but they aren't as popular thus far. Just look for anything with balance in the name if you're looking for one of these.
Armor Revamp is a fairly new one attempting to address concerns with heavy infantry being perhaps too easily killed due to having severe fatigue issues due to armor encumbrance. Basically this one changes encumbrance values of most non-magical armors and one or two magical ones, and that's it.
Endgame Diversity Mod is an attempt to bring more options to the late game, which otherwise tend to be dominated by a very small number of options which are just outright better than everything else and limited to just two magic paths, forcing everyone to develop them or lose in late game (applies to multiplayer only). Endgame Diversity is still fairly new, but is being used more and more in multiplayer.
There are some good nation mods laying around, too. Most of them can be found
here. Especially anything by sombre and burnsaber. Their nation mods and llamabeast's Tomb Kings are the most commonly played in multiplayer. And pretty damn fun, too
They tend to hover somewhere between middle end and high end nations in power. And are stacked with exceptionally well-done graphics.
The mods and maps section of this forum has a number of other nation mods as well. There's a lot of new mods that have been added lately that aren't listed in the mod list, so take your time when looking through that forum. The mod list is a good place to start though. Many people like Amos' mods, for example, though their balance is... questionable, at best. Some of them can make for good AI opponents, though
Last but not least, Burnsaber has made a number of other mods that can be found here or on the other website I linked with a goal of changing up gameplay a bit. UWGIM is a mod designed to make it easier for underwater and land nations to interact with (and kill) one another. Some aspects of this have been rolled into CBM from above. Others include CrossPathCombatSpells, adding a number of spells to take better advantage of low level crosspath mages and give them something to do. Or the Holy War mod, which adds in things like holy magic sites with more recruitable sacreds.
I hope this helps!