All moves with a semi-invulnerable turn can still be hit by Helping Hand, a move following Lock-On or Mind Reader, Toxic if used by a Poison type in Gen VI+, or if either the attacker or target has No Guard (except for a few niche cases).
Bounce
Gust
Hurricane
Sky Uppercut
Smack Down
Thousand Arrows
Thunder
Twister
Dig
Bide (Gen 1)
Earthquake
Fissure
Magnitude
Roar (Gen I)
Swift (Gen I)
Transform (Gen I)
Whirlwind (Gen I)
Dive
Surf
Whirlpool
Fly
Bide (Gen I)
Gust
Hurricane
Sky Uppercut
Smack Down
Swift (Gen I)
Thousand Arrows
Thunder
Twister
Whirlwind (Gen II)
Sky Drop
Gust
Hurricane
Sky Uppercut
Smack Down
Thousand Arrows
Thunder
Twister
Phantom Force and Shadow Force can only be hit by the universal cases listed at the top of this answer.