I'm re-painting a room. The trim (baseboards, door frame, window sills, etc) is all oak... or some kind of wood.

Rather than replacing it all, is there any reason I should NOT just paint over it?

If they were stained and varnished, paint over them first with a good stainkill or your paint will chip off every time they are bumped.

Quoted: Quoted: If they were stained and varnished, paint over them first with a good stainkill or your paint will chip off every time they are bumped. I thought about that but he said "re-painting."

Re-painting the room. Not the trim.
The trim is still "wood looking".
I kind of assumed it was that pre-stained trim you can buy, but I don't know. It was in the house when we bought it. I assume because the majority of the floors are hardwood and it matches. But I plan on laying a piece of carpet in the room so the wood trim really doesn't go with the planned "look" of the room.

If the wood is truly oak, you may have trouble painting it.  Oak has very large open pores.  When painted, these pores result in a surface texture that many find objectionable.  

The pores have to be filled before finishing with a surface finish (varnish, paint, etc.) but this takes a lot of extra time.  

If the wood is unfilled oak, you will likely be better off removing it and replacing it with new, pre-primed trim.

Put another way, if the wood has a smooth surface then paint away.  If it has a super rough surface, replace it.