Good rule of thumb is no more than 30% of the tree, start with the suckers (long straight bows, that shoot straight up).
Remember that apples will grow on wood produced the previous year, so always leave a good proportion (say 50%) of the previous year's growth(evident with a knuckle spur and a small branch containing a few leaves, typically about 2" in length). Its also a good time to prune back the branches near last years buds in an effort to have the limb go in the direction that will open the inner canopy for as much sunlight as you can get. I prune the buds in an effort to keep the limbs horizontal with as little vertical growth as possible, but beware, low limbs will sag with a heavy fruit concentration, limiting mower access in the late summer and early fall. The benefit is you don't have to reach far from your seat to grab an apple as you mow!