Question

What TMs can be picked up with the ability Pickup?

Answer 1

In Pokémon FireRed and LeafGreen, TM10 (Hidden Power) has a 5% chance of being obtained through Pickup at any level.

In Pokemon Emerald, Pokémon XD: Gale of Darkness, and Pokémon Diamond, Pearl, and Platinum, quite a few TMs were obtainable through Pickup at a 1% chance, being TM44 (Rest) from Levels 51-70, TM01 (Focus Punch) from Levels 71-90, and TM26 (Earthquake) from Levels 91-100.

In Pokémon HeartGold and SoulSilver, TM56 (Fling) from Levels 51-70, TM86 (Grass Knot) from Levels 71-90 and, once again, TM26 (Earthquake) from Levels 91-100, at a 1% chance, are all obtainable through Pickup.

In all other games, TMs cannot be obtained through Pickup.

Source

Answer 2

After generation IV, Pokémon with Pickup can no longer pick up TMs, this is because there is no need to seeing as TMs can be reused beginning in generation V.

Source

Answer 3

No tms are available by pickup from Black and White on. Earthquake Focus punch and rest where available by pickup in emerald, diamond, pearl, and platinum. and earthquake grass knot and Fling where available by pick up in HG and SS.

Source: http://bulbapedia.bulbagarden.net/wiki/Pickup_(Ability)