Moves with a high critical hit chance (found here)
If the Pokemon is holding a:
Stick / Leek (Sirfetch'd, Farfetch'd)
Lucky Punch (Chansey)
If the Pokemon has the ability Super Luck, or Merciless (if the target is poisoned).
If you use a Dire Hit / Dire Hit 2 / Dire Hit 3 on a Pokemon.
If the Pokemon has used:
G-Max Chi Strike
If the Pokemon has consumed a Lansat Berry.
If the Pokemon has high Affection which is not Friendship or Happiness or whatever it's called.
The Abilities Battle Armor and Shell Armor prevent Pokémon from landing critical hits on the Pokémon with that Ability. Lucky Chant prevents Pokémon from landing critical hits on the Pokémon it is protecting.
The moves Storm Throw, Frost Breath, Zippy Zap, Surging Strikes, and Wicked Blow will always result in a critical hit (unless prevented by one of the above effects). The move Laser Focus guarantees the next move to score a critical hit.
Hope this helps! :)