Ok, here we go.
All classes are mirror from the opposite faction, so if you divide these numbers by 2, you will get the total number of unique classes and talent trees in the game.
16 Classes (These branch off from the base classes, but are 100% their own class)
Bounty Hunter Powertech
Bounty Hunter Mercenary
Sith Warrior Juggernaut
Sith Warrior Maruader
Imperial Agent Operative
Imperial Agent Sniper
Sith Inquisitor Assassin
Sith Inquisitor Sorcerer
Jedi Knight Guardian
Jedi Knight Sentinal
Trooper Vanguard
Trooper Commando
Jedi Consular Sage
Jedi Consular Shadow
Smuggler Scoundrel
Smuggler Gunslinger
32 specific talent trees (specs) that can only be used by one of the classes (ACs), and not both
Shield Tech
Advanced Prototype
Arsenal
Bodayguard
Vengeance
Immortal
Annihilation
Carnage
Concealment
Medic
Marksmanship
Engineering
Deception
Darkness
Lightning
Corruption
Vigilance
Defense
Watchman
Combat
Tactics
Shield Specialist
Gunnery
Combat Medic
Telekinetics
Seer
Infiltration
Kinetic Combat
Saboteur
Sharpshooter
Sawbones
Scrapper
8 specific talent trees (specs) that can be used by 2 classes (ACs that branch from the same specific standard class)
Firebug
Rage
Lethality
Madness
Focus
Assault Specialist
Balance
Dirty Fighting