What exactly do you mean by "staying in shape"? Like building or maintaining muscle? If you ride correctly everyday this will help maintain your muscle and fitness, however if you cannot ride daily then that doesn't work. If you want to help gain more muscle, you can do excercises both mounted and unmounted.
First, a good mounted excercise is posting with out irons (assuming you ride english). Only attempt if your horse is well behaved, if not have a helper put the horse on a lunge. Start at a walk. Yes, this is extremely harder then it sounds and you will feel, ermmm... very awkward (I do anyways). When comfortable, move into a trot.
I do a lot of unmounted excercises just to stay in good shape anyways. Jogging and running up hills is an effective way to build lower body muscles and tighten and strengthen your core. Do lot's of lunges, squats, and doing simple yoga really improves my balance and strength.
KEEP HORSES IN THE STABLE & OFF THE TABLE !!!!! ♥♥♥