Note that after you unlock the second subclass for one character, it will be unlocked for any new character of the same class that you make in the future.
The third subclass for each class is released after The Taken King expansion. They are unlocked after completing a class specific quest.
Titan Subclasses
Striker
Striker is a Titan subclass that players start off with. Striker utilizes Arc abilities.
Defender
Defender is a Titan subclass that players unlock at level 15. Defender utilizes Void abilities.
Sunbreaker
Sunbreaker is a Titan subclass that will come with The Taken King. Sunbreaker utilizes Solar abilities. It is unlocked after completing the Titan quest ??.
Hunter Subclasses
Gunslinger
Gunslinger is a Hunter subclass that players start off with. Gunslinger utilizes Solar abilities.
Bladedancer
Bladedancer is a Hunter subclass that players unlock at level 15. Bladedancer utilizes Arc abilities.
Nightstalker
Nightstalker is a Hunter subclass that will come with The Taken King. Nightstalker utilizes Void abilities. It is unlocked after completing the Hunter quest ??.
Warlock Subclasses
Voidwalker
Voidwalker is a Warlock subclass that players start off with. Voidwalker utilizes Void abilities.
Sunsinger
Sunsinger is a Warlock subclass that players unlock at level 15. Sunsinger utilizes Solar abilities.
Stormcaller
Stormcaller is a Warlock subclass that will come with The Taken King. Stormcaller utilizes Arc abilities. It is unlocked after completing the Warlock quest The Stormcaller's Path.