Due to a lengthy cooldown and the use of a reagent, this spell should only be used in emergency situations.
The spell's unique advantage over other classes' resurrection spells is that it allows resurrection during combat (in fact most players refer to the spell as "Battle Res" instead of "Rebirth"). From a balance point of view this explains why Blizzard put the 20 minute cooldown on it (30 mins prior to patch 2.3). Without a significant cooldown it could be possible for a raid that has nearly wiped to be completely resurrected without breaking combat with the boss.
In raids, another common use would be to resurrect a tank that has been killed so that they can regain aggro on either the boss or any adds that may be present. However you must remember to heal the tank as quickly as possible, or he may be one shotted immediately after picking up mobs.
Rebirth can be used for wipe recovery. If a party is going to wipe and a member of a class with a resurrection spell has already died, the Druid can cast Rebirth on that player. The player receiving the Rebirth can wait until after the wipe to accept the resurrection and then continue to resurrect the rest of the party. This is an unconventional use of Rebirth and should only be done with good communication, as it achieves no benefit and wastes the cooldown if the resurrected player accepts before the wipe is complete. Also note that you must rebirth the player outside of the aggro range of any enemies or they will be attacked again after they accept. Make sure the healer you use this tactic with doesn't have any mods that auto-accept resurrection spells!
On very rare occasions, the threat attached to restoring X hitpoints to a player, along with their life, can cause an aggro switch.
Should you ever feel generous enough to rez a corpse found at the side of the road, check to see if it's flagged PvP first!