Hey - I currently have 4x hunters + 1x priest (horde), currently lvl 47/48. The main reason to bring a healer is for the rez and gives you much more leeway when you make a mistake. Highly viable in instances, and incredible survivability once you add a healer.

I can't speak to shamans, but priests have a few advantages:
Power word: Shield - has saved my behind so many times, especially when someone gets critted
Prayer of healing/holy nova - essentially heals 8 toons (hunters+pets)
Power word: Fortitude, Divine Spirit, Shadow Protection - some of the best buffs in the game, and you can buff your pets for even more survivability
Dispels/Abolish Disease: incredibly underrated. I play on a pvp server with tons of mages, so being able to dispel their shields just makes taking them down so much easier. I'm talking mainly against lvl 60 mages, who are really your only danger at this point due to aoe damage.