Lots of classes have something along the lines of an increased damage phase against high health targets. In addition to the ones Davesignal mentioned (Firestarter, Big Game Hunter, Careful Aim), I would also include the Shadowpriest (PvP) talent: Initiation.
Hunters, Mages, Warlocks, Priest, Druids, and Shamans have a variation of that same talent: increased crit chance on targets above 80% hp.
Another good example of an Initation though is the old Glyph of Freezing Trap for hunters, which would grant the Hunter 100% critical chance against targets in your traps.
That may not sound like an initiation, but often the way it worked in PvP (where it was typically used), was that you would run a CC chain on the enemy healer (arenas), and when you ran out of CC and your target was still up, you would swap to the healer (in your trap): Aimed Shot+Chimera shot would both hit at the same time and both benefit, so you could auto-crit two of your hardest hitting abilities off the swap. Functionally it was an initiation, though I guess technically it didn't require high HP to do.
What I'm saying is that it would be cool if, rather than giving everyone an Execute and watering it down - they took some away - but gave some classes an Initiate type ability (not just a % crit buff), something that only worked on high HP targets.
A good example I think, would be to give someone like Rets an ability that does double damage while a target is above 80% hp (ex. Templar's Verdict): so they have a big incentive to go hit the newest adds that spawned, but once they're below 80% they ideally would prefer to target swap to a newer add. The reverse would be Shadowpriests with SW: Death, where we would want to be seeking out the lowest hp mobs and persuading them to give up on life.
This adds more variety of priorities, and prevents the somewhat awkward situation we have right now where an add hits 35%, and then suddenly like 25 different people cast some kind of execute on it, and it explodes - classes for whom this was historically a niche (ex. Shadow< Warriors) feel less impactful as a result.