Question

Do TMs pass down through breeding?

Answer 1

In Gen 2 to 5, if the father in the breeding pair knows a TM move that the offspring species is compatible with, then the offspring can inherit that TM move through breeding. This also works for gender-unknown Pokemon breeding with Ditto.

In Gen 6 onward, TMs do not pass down through breeding in any circumstance (unless, of course, the move is applicable to a different inheritance method e.g. egg move).

Source

Comments

Why must it be the father?

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It must be the father because only the father can pass down moves.

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I believe that in X and Y it was changed so that the mother can pass down moves as well. Although this question didn't specify a gen.

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Only with Ditto, though. I think. :3

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In X and Y, both parents of all Pokemon can now pass on TM moves. Not just Ditto. This has been changed since generation 6.

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All the above comments are missing certain details. I've updated the answer with correct information.

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Does this work everytime for all TMs that the offspring can learn by using TM?

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Technically, no. As outlined in the Bulbapedia article linked in the answer, different inheritance methods are "preferred" over others when >4 moves are available to the offspring. In particular, Volt Tackle inheritance means you cannot say it works "every time".
If the above does not apply, then yes, all compatible TM moves known by the father will always be passed down.