Common Moves

For a list of commonly used support moves, look at the following page: Common Support Moves

Reliable moves (80~100 BP, 100 Accuracy)
These moves are used often, being reasonably powerful while retaining perfect accuracy. A mainstay if you don't like risking those pesky misses.

Special

Aeroblast - 90BP - Wind - +2 crit
Dark Pulse - 80BP - Dark - Flinch
Discharge - 80BP - Wind - Paralyze target
Earth Power - 90BP - Earth - SDef drop
Energy Light - 80BP - Nature - SDef drop
Flamethrower - 90BP - Fire - Burn target
Hyper Voice - 95BP - Dream - Nothing
Ice Beam - 90BP - Ice - Freeze
Lava Plume - 80BP - Fire - Burn target
Mana Burst - 90BP - Reason - SDef drop
Nature Sound - 95BP - Nature - Nothing
Poison Bomb - 95BP - Miasma - Poison target
Shadow Ball - 90BP - Ghost - SDef drop
Signal Beam - 90BP - Heart - Confuse target
Sonicboom - 80BP - Steel - SDef drop
Surf - 95BP - Water - Nothing
Thunderbolt - 90BP - Wind - Paralyze target
Tri-Attack - 80BP - Heart - Para/Freeze/Burn target

Physical

Body Slam - 85BP - Heart - Paralyze
Crunch - 80BP - Beast - Def drop
Drawn Line - 80BP - Steel - +2 crit
Earthquake - 100BP - Earth - 2x damage on Dig
Force Palm - 80BP - Faith - Paralyze
Heart Break - 80BP - Dark - Nothing
Ice Ball - 90BP - Ice - Def drop
Leaf Blade - 90BP - Nature - +2 crit
Poison Jab - 80BP - Miasma - Poison target
Return - 102BP - Illusion - Nothing (Only use if you have nothing else to use)
Sculpture - 95BP - Steel - Never misses, Bypasses Detect
Slash - 90BP - Beast - +2 crit
Soar - 90BP - Flying - Can hit through Fly/Bounce
Submission - 85BP - Dream - Nothing
Strength - 80BP - Dream - Raise Attack
Vital Throw - 80BP - Heart - -1 priority, remove held item
Waterfall - 80BP - Water - Flinch

Powerful moves (100~120 BP, 70~90 Accuracy)
These moves pack quite an oomph behind them and will usually do some big numbers, possibly netting more 2HKOs than the above moves do. You gotta risk missing if you decide to use them, though. Moves here with 100 BP have perks which make them viable, such as their secondary effect, coverage, or simply being the best in their class.

Special

Ancientpower - 120/80 - Earth - Raise Defense
Blizzard - 120/75 - Ice - Freeze target
Energy Ball - 120/75 - Dream - SDef drop
Fire Blast - 120/80 - Fire - Burn target
Heat Wave - 100/90 - Fire - Burn target
Hydro Pump - 120/85 - Water - Nothing
Hyper Beam - 120/80 - Dark - SDef drop
LUNATIC - 120/80 - Steel - SAtk drop
Luster Purge - 120/80 - Reason - SDef drop
Mist Ball - 120/80 - Heart - Acc drop
Silver Wind - 120/80 - Faith - Speed drop
Thunder - 120/70* - Wind - Paralyze target, 100% acc in rain

Physical

Battle Chant - 100/85 - Steel - Raise Attack
Braver - 120/80 - Steel - Def Drop
Cross Chop - 100/85 - Dream - +2 crit
Dynamicpunch - 120/80 - Dream - Confuse
Gunk Shot - 120/75 - Miasma - Poison target
Killing Bite - 100/80 - Beast - Flinch
Meteor Mash - 120/80 - Steel - Speed drop
Outrage - 120/80 - Dark - Flinch
Power Whip - 120/85 - Nature - Nothing
Rock Wrecker - 120/80 - Earth - Raise Defense
Sacred Fire - 100/85 - Faith - Raise Attack
Steel Fist - 100/85 - Steel - Defense drop

Priority moves
Need to plink that last 15% off that foe with +3 Tailwind? These moves probably have your back. Aside from Feint and Extremespeed, all the moves below are 40 BP.

Physical

Aqua Jet - Water - +1
Blade Flash - Steel - +1
Extremespeed - Illusion - +1 (80 BP)
Feint - Illusion - +2 (30 BP, bypasses Detect)
Ice Shard - Ice - +1
Mach Punch - Dream - +1
Quick Attack - Flying - +1
Rock Bullet - Earth - +1

Special

Gale - Flying - +1

Recoil moves
Powerful and accurate, but cause the user to suffer some recoil damage if they don't have Rock Head. All of these moves are physical.

Brave Bird - 120/90 - Flying
Double Edge - 120/90 - Beast
Flare Blitz - 120/90 - Fire
Head Smash - 120/90 - Earth
Volt Tackle - 120/90 - Wind

Overheat moves
140 BP and 90 Accuracy, but lower the user's Special Attack by two stages. They hurt when used properly. All of these moves are special.