We don’t know the final count yet, but the ones that were in the Unearthed Arcana playtests were:
Barbarian:
• Berserker
• Wild Heart (formerly called Totem Warrior)
• World Tree (new, does teleportation and plant growth stuff)
• Zealot
Bard:
• Dance (new, focused on unarmed fighting)
• Lore
• Valor
• Glamor
Cleric:
• Life
• Light
• Trickery
• War
Druid:
• Land
• Moon
• Sea (new, focused on aquatic themed stuff)
• Stars
Fighter:
• Battlemaster
• Brawler (was new, focused on unarmed fighting, confirmed to have been cut)
• Champion
• Eldritch Knight
• Psi Warrior (confirmed in the video being discussed)
Monk:
• Elements
• Hand (formerly called Open Hand)
• Mercy
• Shadow
Paladin:
• Ancients
• Devotion
• Glory
• Vengeance
Ranger:
• Beastmaster
• Fey Wanderer
• Gloomstalker
• Hunter
Rogue:
• Arcane Trickster
• Assassin
• Swashbuckler
• Thief
• Psi Knife (confirmed in the linked video; speculated one of the others might be cut to make room for it, since we previously thought each class would be getting 4 subclasses and this would add up to 5)
Sorcerer:
• Aberrant Mind
• Clockwork Soul
• Draconic Ancestry
• Wild Magic
Warlock:
• Archfiend
• Celestial
• Fey
• Great Old One
Wizard
• Abjurer
• Diviner
• Evoker
• Illusionist
• At one point, Jeremy Crawford “confirmed” Necromancer but later walked it back. Speculated Necromancer might show up in the DMG like how the Death Cleric and Oathbreaker Paladin did in the 2014 DMG.