My main stack compostion is as follows, it is based on medieval techs as I normally have won a domination victory when playing my favourite warmonger, Cyrus the Great.
8 Knights (1 led by GG)
4 War Elephants
8 Trebuchets
4 Crossbowmen
A few macemen
I always tilt towards Knights for my campaigns, mainly for the speed, and mainly because I like to upgrade my experienced Immortals. Cyrus is pretty much the best for warring.
I'm not sure that knights are the best units for this, actually. Knights seem to me to be best suited towards pillaging, particularly if escorted by a mace to counter spears/pikes. That way you can move and pillage in the same turn.
For most other things, I'd think that there are cheaper, more effective units. This is primarily because city-raiding stacks move as quickly as the slowest unit. Typically this is also the most important unit, the trebuchet or catapult.
Knights kill longbowmen and crossbowmen, when in the field. That's a good use for the. BUT, to defend your stack, spears/pikes/elephants > knights (as they're cheaper/stronger) vs cavalry, crossbows > knights vs melee (maces/pikes), and maces > knights vs cities. (cheaper and get CR) Of course, trebs and cats are the best vs cities, backed up by maces with CR.
Sure, your knights can get to a city before an army composed primarily of foot-slogging maces and catapults, but knights are going to have real issues taking a longbow defended city without cat. support. Longbow defensive bonuses are just too good, even without the first strikes. If you're fighting archers with knights, then you're so far ahead stack composition isn't really a big issue.