Normal:
* Peck
* Gust
* Drill Peck
* Quick Attack
* Aerial Ace
* Brave Bird
* Sky Attack
Flying:
* Air Slash
* Hurricane
* Feather Dance
Electric:
* Thunder Wave
* Thunderbolt
* Thunder
Fighting:
* Brave Bird
* Quick Attack
* Double-Edge
Ghost:
* Shadow Claw
* Shadow Ball
Ice:
* Ice Beam
* Freeze-Dry
Poison:
* Poison Jab
Ground:
* Earthquake
Rock:
* Rock Blast
Steel:
* Iron Head
Dark:
* Crunch
* Foul Play
Bug:
* Bug Buzz
Fire:
* Heat Wave
* Flamethrower
Water:
* Hydro Pump
* Muddy Water
* Surf
Grass:
* Razor Leaf
Dragon:
* Outrage
Psychic:
* Future Sight
* Psycho Cut
* Psybeam
Status Moves:
* Roost
* Defog
* Tailwind
* Substitute
* Will-O-Wisp
* Toxic
* Protect
This is not an exhaustive list, but it highlights the broad range of moves Pidgeot can learn. You can see a more comprehensive list of Pidgeot's moves on various Pokemon websites or in the Pokemon games themselves.
Keep in mind that moves can be taught by TMs, TRs, breeding, and by learning them naturally as Pidgeot levels up.