This is an attempt to document every Pokémon battle technique existing. I will keep adding to this as time goes by.

Absorb - Grass attack. Sucks a small amount of health from the enemy and transfers it to your Pokémon.
Acid - Poison. Causes damage, sometimes lowers enemy's Defense.
Acid Armor - Poison. Raises your Pokémon's defense.
Agility - Psychic. Greatly raises your Pokémon's speed.
Amnesia - Psychic attack. Raises your Pokémon's Special.
Aurora Beam - Ice type. Causes damage and may lower the enemy's Attack. Also, as with all Ice attacks, it has the power to freeze the enemy.

Barrage - Normal type, causes damage in a way similar to Fury Attack.
Barrier - Psychic attack. Raises your Pokémon's Defense.
Bide - Normal attack. Absorbs damage from two turns and pays it back double. Found in TM 34.
Bind - Normal. Causes damage in a way similar to Fury Attack.
Bite - Normal-type attack. Causes damage, sometimes causes the enemy to "flinch", or miss it's attack turn.
Blizzard - Ice attack also found in TM 14. Causes damage.
Body Slam - Normal. Causes a lot of damage and may paralyze the enemy, also found in TM 08.
Bone Club - Ground attack. Causes damage.
Bonemarang - Ground. More powerful version of Bone Club.
Bubble - Water-type attack. Causes damage, sometimes lowers enemy's speed.
Bubblebeam - Water attack. More powerful than Bubble, found in TM 11.

Clamp - Water. Causes damage similar to Wrap.
Comet Punch - Normal attack that causes damage in a way similar to Fury Attack.
Confuse Ray - Ghost attack that confuses the enemy. Has a higher success rate than Supersonic.
Confusion - Psychic attack. Causes damage and sometimes makes the enemy confused, causing it to attack itself.
Constrict - Normal attack. Works similar to Wrap, but only attacks for one turn and may paralyze the enemy. This attack doesn't seem to have much use...
Conversion - Normal. Your Pokémon switches it's type to match the enemy's.
Counter - Fighting attack. Deals twice the damage you've recieved so far, but only for physical attacks.
Crabhammer - Water attack that causes basic damage.
Cut - Normal attack. Is pretty powerful, also can cut down bushes on the map screen. Found only in HM 01.

Defense Curl - Normal. Raises your Pokémon's defense.
Dig - A Ground-based attack. Your Pokémon digs underground, making the enemy's attack miss, then on its next turn your Pokémon comes out of the ground and causes a lot of damage. This move can also be found in TM 28.
Disable - Psychic type. Causes a random attack on the enemy's attack list to be disabled for a few turns.
Dizzy Punch - Normal. Causes damage.
Double Kick - Fighting. Causes damage; hits twice.
Double Team - Normal. Increases your Pokémon's Evade. Also found in TM 32.
Double-Edge - Normal type. Causes a lot of damage but also hits your Pokémon with "recoil", causing it to lose a few HP. Also found in TM 10.
Doubleslap - A Normal-type move that causes damage.. Works like Fury Attack.
Dragon Rage - Dragon attack (duh!) Causes damage.
Dream Eater - Psychic attack also found in TM 42. Causes major damage, and gives 1/2 the HP to your Pokémon. One catch: the enemy must be asleep.
Drill Peck - Flying attack. Causes damage.

Earthquake - Ground attack also found in TM 26. Causes regular damage.
Egg Bomb - Normal attack. Causes damage. Found only in TM 37.
Ember - Fire attack. Causes damage, sometimes burns the enemy.
Explosion - Normal attack. A more powerful version of Self-Destruct, also found in TM 47.

Fire Blast - The best Fire attack. Found in TM 38.
Fire Punch - Fire attack. Causes damage and may, as with all Fire attacks, burn the enemy.
Fire Spin - The most powerful Fire attack, except for Fire Blast.
Fissure - Ground attack. If it is successful, it will defeat the enemy in one hit. Found in TM 27.
Flamethrower - Fire attack. Causes more damage than Ember.
Flash - Normal attack. Decreases the enemy's accuracy and is also used to light up dark areas. Found in HM 05.
Fly - Flying. Your Pokémon flies up, causing the enemy's next attack to miss, then causes damage. Also used for instantaneous transportation to any city you've previously visited. Found in HM 02.
Focus Energy - A Normal attack. I can't figure out how this thing works....
Fury Attack - Normal type. Attacks the enemy anywhere from twice to five times in a single turn.
Fury Swipes - A Normal attack. Combination of Fury Attack and Scratch, in that it attacks from 2 to 5 times, but each time causes the same amount of damage as Scratch would.

Glare - Paralyzes the enemy.
Growl - A Normal attack. Lowers the enemy's attack power.
Growth - Raises your Pokémon's Special. A Normal attack.
Guillotine - Normal. If successful, as with Fissure, it will defeat the enemy with one hit.
Gust - A Normal attack. Causes damage.

Harden - A Normal-type attack. Raises the defense of your Pokémon.
Haze - An Ice attack. Cancels all effects (sleep, poison, paralysis, etc.) on both Pokémon.
Headbutt - A Normal attack. Causes damage and may cause the enemy to "flinch".
Hi Jump Kick - Fighting attack. Causes damage, but if your Pokémon misses, it will recieve 1/8 the damage the attack would have caused.
Horn Attack - Normal typed attack. Causes about the same amount of damage as Scratch.
Horn Drill - A Normal attack also found in TM 07. If successful, as with Fissure, it will defeat the enemy with one hit.
Hydro Pump - The most powerful Water attack, aside from Surf.
Hyper Beam - Normal attack. No further information available.
Hyper Fang - Normal. Causes a lot of damage.
Hypnosis - Psychic attack. Causes the enemy to fall asleep.

Ice Beam - Ice attack. Causes damage, of course also has the potential to freez the enemy. Also found in TM 13.
Ice Punch - Ice attack. Causes damage and can freeze the enemy.

Jump Kick - Fighting. Causes damage, but there is one drawback. If your Pokémon misses, it will recive 1/8 the amount of damage the enemy would have recived.

Karate Chop - Surprisingly, a Normal move. Causes damage.
Kenesis - Psychic. Lowers the enemy's accuracy.

Leech Life - Bug attack. Sucks a small amount of health from the enemy and transfers it to your Pokémon.
Leech Seed - A Grass attack. After the enemy has beed "seeded", it loses a small amount of health to your Pokémon each turn.
Leer - Decreases the enemy's defense. Normal-typed.
Lick - Ghost. Causes minor damage and sometimes paralyzes the enemy.
Light Screen - Psychic attack. Reduces the amount of damage recived from Special attacks by 50%.
Lovely Kiss - The weirdest-named attack ever. This Normal-type attack causes the enemy to fall asleep.
Low Kick - Fighting. Causes damage and may cause the enemy to "flinch".

Meditate - Psycic. Increases your Pokémon's Attack.
Mega Drain - Grass. A super-powered version of Leech Life.
Mega Kick - Fighting. Also found in TM 05, causes damage.
Mega Punch - Fighting. Also found in TM 01, causes damage.
Metronome - Normal attack. This attack uses a random TM every time. Also found in TM 35.
Mimic - Found in TM 31. This attack allows your Pokémon to temporarily learn one of the enemy's attacks.
Minimize - Increases your Pokémon's Evade. Normal attack.
Mist - Ice attack. Defends your Pokémon against Special attacks that reduce abilities, i.e. Kenesis.
Mirror Move - Flying attack. Copies whatever the enemy did on its last turn.

Night Shade - Ghost. Causes damage.

Pay Day - a Normal attack. Causes damage, but also causes coins to fall on the floor. After you beat the Pokémon, you can pick up money off thr ground.
Peck - A Flying attack. Causes damage.
Petal Dance - Grass. Deals damage but confuses your Pokémon.
Pin Missile - Bug. Causes more damage than Twineedle.
Poison Gas - Poison. Poisons the enemy.
Poison Powder - Grass. Poisons the enemy.
Poison Sting - Poison-type attack. Causes damage and sometimes poisons the enemy.
Pound - Normal attack. Causes damage.
Psybeam - Psychic attack. Causes damage and may confuse the enemy.
Psychic - Psychic attack also found in TM29. Causes damage and may confuse the enemy.
Psywave - Psychic attack found only in TM 46. It deals a lot of damage.

Quick Attack - Normal attack. Causes damage. Also this attack will always go first in battle.

Rage - Normal-type attack. Once used, that is the only attack you can use until either your Pokémon or the enemy faints. The more your Pokémon is attacked, the higher its Attack rises.
Razor Leaf - Grass attack. Causes damage.
Razor Wind - Normal attack found in TM 02. A Two-turn attack that causes damage.
Recover - Ahh, the all time favorite. This Psychic attack recovers half of your Pokémon's max HP.
Reflect - Psychic attack. Reduces all damage dealt to you from physical attacks by 1/2.
Rest - Replenishes your Pokémons HP to the max, but also causes it to fall asleep. Also found in TM 44.
Roar - Normal. "Scares" the enemy away.
Rock Slide - Rock attack. More powerful version of Rock Throw, but has a better accuracy. This attack is found only in TM 48.
Rock Throw - Rock. Causes damage; this attack seems to have a lower accuracy than others.
Rolling Kick - Fighting. Causes damage and may make the enemy "flinch".

Sand-Attack - Decreases the enemy's accuracy. Normal-type.
Scratch - Normal attack. Causes more damage than Tackle.
Screech - Normal type attack. Greatly lowers the enemy Pokémon's defense.
Seismic Toss - Fighting. Causes damage.
Self Destruct - Normal. Causes a lot of damage to the enemy, but also causes your Pokémon to faint.
Sharpen - This Normal-type move raises your Pokémon's Attack.
Sing - Normal. Causes the enemy to fall asleep.
Skull Bash - Normal two-turn attack. Causes lots of damage. Also found in TM 40.
Sky Attack - Flying two-turn attack. Causes damage.
Slam - Normal. Causes damage.
Slash - More powerful Scratch. Normal-type.
Sleep Powder - Grass. Causes the enemy to fall asleep.
Sludge - Poison attack. Deals damage and may poison the enemy.
Smog - Poison. Causes damage and may poison the enemy.
Smokescreen - Normal attack. Lowers enemy's accuracy.
Softboiled - Normal attack found only in TM 41. No further information.
Solar Beam - A powerful Grass-type attack. Takes one turn to charge up, and then lets out the attack. Also found in TM 22.
Sonic Boom - A Normal attack. Seems to be a more powerful version of Gust.
Spike Cannon - Normal. Causes damage in a way similar to Fury Attack.
Splash - Water. This attack does absolutely nothing. Of course, it's Magikarp's only attack! ^_^
Spore - Grass. No further information available.
Stomp - Normal attack. Causes damage and may make the enemy "flinch".
Strength - Normal attack. Causes damage, also is used while moving in the world to move rocks. Found in HM 04.
String Shot - A Bug-type attack. Decreases the enemy's speed.
Struggle - Used automatically when all your Pokémon's PP is gone, but your Pokémon recives 1/4 the damage the enemy recieved.
Stun Spore - Grass attack. Paralyzes the enemy.
Submission - Fighting. A super version of Take Down or Double Edge. Also found in TM 17.
Subsitute - Normal attack also found in TM 50. I'm not exactly sure how it works, but it seems like a "decoy" is created, but not with full health. The enemy attacks the decoy, and you attack the enemy. After the decoy faints, your Pokémon is sent back out.
Super Fang - More powerful than Hyper Fang. A Normal attack.
Supersonic - Normal attack. Causes the enemy to become confused and start attacking itself.
Surf - Water attack. Causes damage, also is used to swim in the ocean. Found in HM 03.
Swift - Normal attack. Causes damage. Is very accurate...also found in TM 39.
Swords Dance - Normal attack also found in TM 03. Greatly raises your Pokémon's Attack.

Tackle - Causes normal damage.
Tail Whip - Decreases the enemy's defense. A Normal-type attack.
Takedown - Normal attack. Works like Double Edge.
Teleport - Psychic attack. Your Pokémon runs from battle when you use this. Also, you can use this ability on the map to take you back to the last Pokécenter you used.
Thrash - A Normal attack. Once you use this attack, you cannot stop.
Thunder - The most powerful Electric attack. Deals damage and may cause paralysis.
Thunder Wave - Electric attack. Paralyzes the enemy. Also found in TM 45.
Thunderbolt - An Electric attack. A more powerful version of Thundershock. Found only in TM 24.
Thunderpunch - Electric. Causes damage and sometimes paralyzes the enemy.
Thundershock - Electric. Causes damage and sometimes paralyzes the enemy.
Toxic - Poison attack found only in TM 06. This attack poisons the enemy, and the damage dealt from poison increases exponentially each turn.
Transform - Normal attack. Turns your Pokémon into a copy of the enemy, with the exact same powers.
Tri Attack - Normal. Causes damage, also found in TM 49.
Twineedle - Bug attack. Works like Doubleslap, but only attacks twice.

Vicegrip - Normal. Causes damage.
Vine Whip - Grass attack. Causes damage.

Water Gun - Water attack. More powerful than Bubble, but does not decrease the enemy's speed.
Waterfall - Water attack. Causes damage.
Whirlwind - Normal attack. Blows the enemy away. This attack has no effect in trainer battles. Also found in TM 04.
Wing Attack - Flying. Causes damage.
Withdraw - Water. Increases your Pokémon's defense.
Wrap - Normal attack. Causes damage over more than one turn, the enemy is immobilized while the attack is being used. Also, if the enemy's level is less than your level, you may see the message "Enemy _____ can't move!" This means that after Wrap wears off, it will still be your attack turn.