Save for Waking Dreams, you'll either get a shout or the option to choose from one of three powers. Some are stat boosts, like making it so you can't cause friendly fire. Others let you do things like summon a Dremora merchant once a day.
Most controversial?
Spoiler Perk respecs - one dragon soul wipes a skill tree completely and lets you respend the points however you please.
<<< Only available post-MQ