Many times when Ash's Pikachu fights a Ground-type Pokémon, it uses an Electric-type move and it will cause damage.
Since the beginning of the Diamond & Pearl series, Electric-type attacks have been consistently shown to have no effect on Ground-type Pokémon.
May's Squirtle attacked and damaged Harley's Banette with Tackle in New Plot, Odd Lot, despite the Ghost type's immunity to Normal-type attacks.
In multiple instances, Shadow Ball is able to hit Normal-type Pokémon, despite being a Ghost-type attack.
Pokémon without Sturdy surviving one-hit knockout moves, like Horn Drill, without fainting.
Some non-damaging attacks cause damage to the Pokémon being attacked, such as Brandon's Dusclops using Will-O-Wisp.
Furthermore, it affected Ash's Charizard which, as a Fire-type Pokémon, should be unaffected by Will-O-Wisp.
Safeguard has been able to protect against attacks instead of status problems.
Light Screen has been able to block physical attacks, even though it usually only affects special attacks.
Similarly, Counter has been shown to block special attacks, even though in the games it only affects physical attacks.
Psychic-type moves have had effect on Dark-type Pokémon, even though Dark-type Pokémon are immune to the effects of Psychic-type moves.
In The Blue Badge of Courage, Psyduck uses Confusion on a Poochyena that belongs to the Gym Badge thieves.
In Zoroark: Master of Illusions, Karl's Bronzor levitated Zorua with Psychic. As a Dark-type Pokémon, Zorua is immune to Psychic-type moves.
Swift, a move that cannot miss in the games, was dodged twice in the anime: first by a Weavile who avoided Swift from Ash's Aipom in Duels of the Jungle, second by Elesa's Zebstrika in Enter Elesa, Electrifying Gym Leader!.
In The Grass-Type Is Always Greener!, Gardenia's Turtwig used Leech Seed on Ash's Turtwig, even though Grass-type Pokémon are immune to the effects of Leech Seed.
In Noodles! Roamin' Off!, a Metagross was damaged by Seviper's Poison Tail, even though Steel-type Pokémon are immune to Poison-type moves.
http://bulbapedia.bulbagarden.net/wiki/Anime_physics
