Update for version 6.0:
With patch 6.0 (Warlords of Draenor expansion), Symbiosis has been removed from the game.
Original post:
Receiving players have no choice in what they get from the druid, and the druid has no choice on what they get from the player. It's all based off class. The most recent lists I've found (dating from the 26th of July, as these have changed a number of times in the beta) are below.
The skill for the non-casting player:
_Class_ _Spec_ _Skill_
Death Knight Blood Might of Ursoc
Frost/Unholy Wild Mushroom Plague
Hunter All Dash
Mage All Healing Touch
Monk Brewmaster Survival Instincts
Mistweaver Entangling Roots
Windwalker Bear Hug
Paladin Holy Rebirth
Protection Barkskin
Retribution Wrath
Priest Discipline/Holy Cyclone
Shadow Tranquility
Rogue All Growl
Shaman Enhance/Elemental Solar Beam
Restoration Prowl
Warlock All Rejuvenation
Warrior Arms/Fury Stampeding Shout
Protection Savage Defense
The skill for the casting druid:
_Class_ _Balance Druid_ _Feral Druid_ _Guardian Druid_ _Restoration Druid_
Death Knight Anti-magic Shell Death Coil Bone Shield Icebound Fortitude
Hunter Misdirection Play Dead Ice Trap Deterrence
Mage Mirror Image Frost Nova Frost Armor Ice Block
Monk Grapple Weapon Clash Elusive Brew Fortifying Brew
Paladin Hammer of Justice Divine Shield Consecration Cleanse
Priest Mass Dispel Dispersion Fear Ward Leap of Faith
Rogue Cloak of Shadows Redirect Feint Evasion
Shaman Purge Feral Spirit Lightning Shield Spiritwalker's Grace
Warlock Unending Resolve Soul Swap Life Tap Demonic Circle: Teleport
Warrior Intervene Shattering Blow Spell Reflection Intimidating Roar
Unfortunately links don't work inside code tags, so if you want to see the details on the skills here are links/tooltips for all of them.