Minecraft wiki entry for Enchanting_mechanics, associated text: Every enchantment conflicts with itself. (The player can't get a tool with two copies of the Efficiency enchantment.)
All damage enchantments (Sharpness, Smite, and Bane of Arthropods) conflict with each other.
All protection enchantments (Protection, Blast Protection, Fire Protection, Projectile Protection) conflict with each other.
Silk Touch and Fortune conflict with each other.
Depth Strider and Frost Walker conflict with each other.
Mending and Infinity conflict with each other.
Riptide conflicts with Loyalty and Channeling.
Multishot and Piercing conflict with each other.