Enchants

Swords:
Withering - Chance to apply withering
EggHunter - Gives you a chance to get mob eggs
Poisonous - Gives you a chance to apply poison
Lifesteal - Gives you a chance to steal some of the enemy's hp
Paralyze - Gives a chance to apply slowness and blindness
Experience - Gives you more experience from killing mobs
Beheading - Gives you a chance to get player heads
Blindness - Gives you a chance to apply blindenss to enemys
DeathBringer - Does more damage to players
IceAspect - Gives you a chance to freeze your enemy's
Worms - Gives you a chance to apply hunger to enemy's
Unarmored - Gives you a chance to take off a piece of an enemy's armor
XPSteal - Gives you a chance to steal your enemy's experience

Tools:
Expedition - Gives you extra XP for mining
Haste - Whenever you hold the tool it gives you haste
OreMagnet - Makes ores pop into your inventory
Reward - Gives you a chance to earn some cool rewards when mining
Crushed - Gives you haste when mining obsidian

Bows:
QuickDraw - Makes arrows shoot faster
EggShooter - Joke enchant makes you shoot eggs
Direct Impact - Makes you negate armor damage
EnderShot - Makes you shoot an enderpearl 10 second cooldown
Restoration - Its essentially a lifesteal for bows

Armor:
Abandon - You have a chance to get speed when getting hit1
Absorb - You have a chance to cancel a hit of damage
Enderborn - You have a chance to get an enderpearl back after throwing it
Fireproof - Negates all fire damage
Glowing - Gives you nightvision
HealthBoost - Increases your health
Jump - Gives you jumpboost
Molten - Has a chance to catch an enemy on fire after hitting you
PoisonProtection - Negates poison damage
Replenish - Gives you regeneration
Saturation - Never eat again
ShockAbsorb - Never take fall damage
Speed - Applies speed boost
Juggernaut - Gives you resistence
Beast - Gives you strength
Undead - Negates mob damage unless you hit them