Any opponent
Me first
Outrage
Uproar
Petal dance
Thrash
All opponents
Acid
Air cutter
Blizzard
Bubble
Dark void
Dazzling Gleam
Electro web
Eruption
Glaciate
Growl
Heal bell
Heat wave
Hyper voice
Icy wind
Imprison
Incinerate
Leer
Muddy water
Poison gas
Powder snow
Razor leaf
Razor wind
Relic song
Rock slide
Snarl
Entery hazards (Stealth Rock, Spikes, etc.)
String shot
Struggle bug
Surf
Sweet scent
Tail whip
Swift
Water spout
All Pokemon
Bulldoze
Discharge
Earthquake
Explosion
Lava plume
Magmatude
Searing shot
Self destruct
Sludge wave
Surf
Synchronise
Teeter dance
All Pokemon
Gravity
Hail
Haze
Magic room
Mud sport
Perish song
Rain dance
Sandstorm
Sunny day
Trick room
Water sport
Wonder room
Self
Ally switch
Follow me
Rage powder
Self or your ally
Acupressure
Ally
Aromatic Mist
Helping hand
Your Team
Aromatherapy
Crafty Shield
Happy Hour
Heal bell
Light screen
Lucky chant
Magnetic Flux
Mat Block
Mist
Quick guard
Reflect
Tailwind
Wide guard
Let me know if I missed any!
Source: http://bulbapedia.bulbagarden.net/wiki/Double_Battle