I use mercenaries for three things.

Mercenaries are primarily for absorbing casualties and filling out a line so your national troops can flank and destroy the enemy and get the Valour. Lovely Italian Light Infantry and pretty much any Muslim foot fill that position nicely.

My secondary use of mercenaries is for throwaway cavalry. In this form they are the disposable RPG of the medieval era, to chase down a thicket of archers or get a quick charge in faster than my knights can get there. Light horse and Horse Archers are preffered, along with Jinettes. When a couple brigades of Khwazariman are going to stomp on my flank a bit before I can break their line, harassing mercenaries force them to chase, and if they ignore them a couple volleys of Javelins will ruin their day, as will being charged in the rear, even if its just by Hobilars. Scotch Highlanders and Irish Gallowglasses do a good job as fire-and-forget weapons too, but I usually am England and pumping them out at a steady pace.

The tertiary use is for filling up on one-use gimmick units without having to payout for the infrastructure. I don't want to have to spend thirty years and thousands of florins to be able to nationalize artillery support for the one or two castles I'll bother assaulting in the course of a game. And Longbows are in scarce supply even when I am playing England, since I have to replace line infantry casualties and replace my fire-and-forget troops on a regular basis. If I see them, I grab them.