Let's see, my favorite schooling exercises are first, working on different speeds within gaits - a decently schooled horse should have two clear, distinct speeds at the walk, three at the trot and canter.
Then, I like to do a lot of serpentines, varying the number and size of loops. A great exercise is to do a very shallow serpentine and turn the horse with your eye, upper body and postion of your legs, no reins and no active leg aid. An advanced exercise is a zig zag, with 1/4 turns on the haunches to change direction. Very good for refining indirect aids and focusing on straightness.
A deceptively simple exercise is to ride the quarter lines of the arena - good check to see if your horse is truly straight, or tends to fall to one side or another without the arena wall. Once you've got that you can leg yield from the quarter line to the rail, and then from the rail to the quarter line.
Stormy Blue's spiral is a good one as well.
You can also work on halt/back/walk and turns on the forehand to keep your horse's focus, and if your horse is at this level of schooling, shoulder in, shoulder fore, travers and renvers.
If you tend to fall in to the trap of just hacking aimlessly arount the ring, write out a lesson plan appropriate for your level and keep it in your pocket. Always have an alternate, easier version of a planned exercise in mind so if the original plan doesn't go as you wanted, you can fall back on an easier exercise and keep your schooling positive.