actually... it depends. Activated abilities have two parts: the cost and the ability itself. The COST is the part on the left side of the ' : ' and the ability on the right side.
You can activate such ability any time you can pay its cost!!! (and of course are not prohibited by any other means like: Arrest or Linvala, Keeper of Silence )
Taping can be part of a cost, signaled by the little turning arrow , ex: Prodigal Pyromancer
others don't have that: Spikeshot Elder
If the cost does not include taping the permanent (that you can't pay with an already tapped permanent), then you can activate the ability (after paying the FULL cost), other vise, you can't.
So from my example, you can't activate the ability of a tapped Prodigal Pyromancer but you can with Spikeshot Elder
