Is it worth taking carbon/puragen out of the filters if your trying to induce breeding? I've heard tannins in the water help and I know Puragen especially takes them out.

IMO take them out and never use them again!

If you are using them then generally there is an imballance in the tank that needs to be fixed properly rather than the carbon bandaid.

I've always had it in there as a cosmetic thing to keep the water clear. Should I take both the Puragen and the Carbon pads out? I've got a Fluval filter that came with carbon pads in the cartriges...

I only use them if i am trying to take something out of the water like excess meds or if i have put in some new wood which is leaching excessive tannins. The problem with them is that they get full and then (carbon especially) will dump it all back into the water in one hit. Thats is why i use it for a week then toss it.

If you dont like the tannins then take your wood out and boil it for a hour or so, this will get the tannins out fast!

Use them only on a need-to-use basis.
As Doug said, after medical treatment you could remove traces of the medication. Otherwise, do not keep in the tank.