I'm guessing early to mid-'90s, and even if they were around that long, they were significantly shorter than they had been in the past.
The last CBS movie intro that I specifically remember was (I think) based on the network's 1992 promotional graphics, and was really little more than a glorified bumper.
All 3 networks had some good intros over the years (ABC's star tunnel intro comes to mind), but for me, CBS was consistently the best.