Doors and Windows - Installing doors

Is it best to install a door before or after the sheetrock has been put up?

After, for sure.

I like to hang the doors before the rock goes up. Once they're hung, remove the doors from the jambs and put them in a safe place.

So long as youre not doing any major work on the surrounding walls.
In my case, I removed the old plaster and lathing for new insulation, VB and drywall.
If I did it your way, I'd be short about 1/4" on my wall, because the drywall was about 1/4" 'thinner' than the plaster and lathing wall.
So it could/would depend on what the reno is all about.
If its just replacing a door, than pre-hund would probably be easier, with new moldings and stops, of course.

Good point, jatco. Lath and plaster is different than drywall (and very rare around here) so other methods may be better. For 1/2" rock (standard stuff here), I use a piece of 1/2" board to align the jambs with 1/2" exposure on the studs and the drywall lines up right on.

I'm totally sold on prehung doors. The time required to set up and cut new hinge mortises (and sometimes realign the old jambs) can easily make prehung doors cost effective.

Absolutely.
Prehung's are easier in the long run...especially on exterior doors.
When I hung 2 new oak interior doors (only) I had the store do the mortises for the hinges using the old doors as a template, as this is what they do and have the good hinge set-up tool. Even with the old doors to work from, they still got the mortises wrong. I had to re-work them myself to get the hinges to match the existing jamb.
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Lath and plaster isnt used up here anymore either. The work I recently did was on the old part of the house, circa 1948. Thats what they used then. Hate it. (Why they call it plaster is beyond me...its concrete, basically).