In Commander, can your commander have a mana cost of zero and still be cast from the command zone?

A commander is cast from the command zone as a special action governed by the Commander rules (rule 903.8). The cost to cast it is its mana cost plus an additional {2} for each previous time it has been cast from the command zone this game — the so-called 'commander tax.'

If a commander's mana cost is {0}, you simply pay {0} to cast it the first time (i.e., nothing), then {2} the second time, {4} the third time, and so on. Having a mana cost of {0} is not the same as having no mana cost; only objects with no mana cost at all (like most land cards) cannot be cast. A printed {0} is a real, payable cost (CR 202.1, 117.6).

Cards like Emrakul, the Aeons Torn have no mana cost and therefore cannot be your commander (CR 903.3c requires a legendary creature card, but also the game cannot let you cast something with no mana cost from the command zone without an alternative cost). By contrast, a legendary creature with a printed mana cost of {0} — such as a hypothetical {0}-cost artifact creature — is perfectly legal and castable.

Concrete example: Suppose your commander has a mana cost of {0}. Turn 1, you cast it from the command zone for free (pay {0}). It dies and returns to the command zone. The next time you cast it, you pay {0} + {2} = {2} total. The time after that, {0} + {4} = {4}, and so on.

Relevant rules: CR 202.1 (mana cost defined), CR 117.6 (paying a cost of zero), CR 903.8 (casting your commander from the command zone), CR 903.8 (commander tax).