Dungeons and Dragons Online's "do over" system, is slated for a revamp with Update 20. When the update lands, there will be four types of reincarnation available to players: heroic true reincarnation, iconic true reincarnation, epic reincarnation, and lesser reincarnation. At the same time, greater reincarnation will be phased out of the game.
These four types of reincarnation reset your levels (either back a few or all the way to level 1) while giving you bonuses like past life feats and more build points for your next run. Epic reincarnation merely resets your epic levels to 20, while iconic reincarnation applies only to the new iconic characters.
There's a great amount of information about this complex system available on the forums, including a look at how different forms of reincarnation will work depending on your class.
[Thanks to Scott for the tip!]