It depends heavily on the faction you are playing IMO, although cavalry seem to dominate in most cases. The best cavalry factions seem to be the Swadians for their strong straight-up attack and the Khergits (obviously) for their ability to both charge straight up and skirmish with their mounted archers. On a side note, there is nothing more annoying than killing off all the Khergit lancers and then having to chase down the remaining skirmishers.
The best way to counter cavalry seems to be having a good, mixed army and most of the infantry as skirmishers (archers preferred). What I like to do is I lead my infantry on top of some hill or in a small forest (pretty much anything that slows cav. down is good), take my horsemen and charge in their cavalry, make them follow me and lead them close to my archer units. When the enemy cavalry is in range of my archers I stop my horsemen and hold the enemy in place while my archers pick them off. Then I do the usual counters to infantry and remaining missile cavalry.
One small note: when facing a much more numerous or better quality cavalry army, you can suffer heavy casualties.