No other role dictates whether a dungeon run will be successful as much as the healer.

The feeling when you make a mistake and it causes a wipe sucks.

The feeling you get when things are going very badly and you manage to heal through the mess and come out successful is fantastic.
The rest of the group may not even realize how close they were to wiping but you do and it feels great.

When things are going badly and you are tanking you are completely at the mercy of the healer to pull you through.
When things are gong badly and you are DPS you pretty much just keep pushing 1-2-3-1-2-3 until the tank/healer pull through, or you die.