Walls and Ceilings - installing trim

I am in the process of finishing my basement, I am getting ready to paint, but should I install the baseboard trim before I paint everything. This is the way I saw the builder do it to the rest of the house. Is there a reason for doing it this way?

I wouldn't. It's much easier to paint the walls if there is no trim on. Some people insist on caulking the edges of their trim with painters' caulk so that there are no "lines" where the trim meets the wall. If that's the look you're going for, then you install all the trim first, caulk the edges with a very fine bead, and then cut around everything with a brush. Personally, I hate cutting edges- its the most time consuming part of painting. I'd much rather install trim that is pre-painted and then just have to touch up the nail holes.

If your baseboard is stained, your roller will spatter your baseboard. In that case, you'd want to mask off the baseboard to keep it clean. Again, easier to leave it off in the first place, in my mind.

If the base board is to be painted I would install it before the finish coat of paint on the wall. Caulking the trim makes for a nice clean professional looking job. If the woodwork is stained, install it last, already finished except for the final coat [just putty the nail holes and one last coat of varnish or poly]