The dungeon tool offers you a quick and easy way to get into a group instead of spamming LFG or begging your guild. That in itself should be reward enough, but there are some bonuses include Atlantica Gold.
Random dungeons in Classic and TBC grant a reward bag with one BoP blue inside of it for the first time you run them. Random dungeons in WotLK give you 2 Emblems of Triumph for the first time you run them. Random WotLK heroics grant you 2 Emblems of Frost and an additional 2 Emblems of Triumph for every time you run it after that.
There are three achievements too. Looking for More is rewarded for grouping with 10 random people (3 dungeon runs). Looking for Many is awarded for grouping with 50 random people (13 dungeon runs). Looking for Multitudes is awarded at 100 random people (25 dungeon runs) and grants the Perky Pug pet.