Other than shouting or physical reinforcement, there is always the option of complete and utter ignorance.
In the case of biting, consider why the biting. If he's seeking attention, ignoring him (thusly giving him nothing, and a lack of 'positive reinforcement' teaches him that biting will get him nowhere, and is pointless.
However, if he's biting in an attempt to assert what dominance he thinks he has, then often a good yell and scream'll do it. ( Note: Horses do vocalize displeasure and anger, with squeals and extended grunts. )
For the persistant biter, physical assertion of yourdominance is usually needed, but [i]always accompanied by a yell or loud 'No!', this way yelling becomes negative reinforcement without the physical contact.
-Remember that smacking/popping/pinching your horse around the head or muzzle is often seen as a game by younger fillies/geldings/colts, and evenmature horses. Just think how much of a giggle they get when they swing their head out of the way and you miss! (You think I'm kidding, but watch play in the field!) And then by the time you've taken a second swipe, he's forgotten what he did wrong! And then of course there's always the chance that you could seriopusly injure your animal if you catch his eye, or he swings his head and catches his hay rack/stable door/(insert other stationary object here).
-If you're going to smack your horse, the best places are the meaty areas around the neck/shoulders/chest.
-If a smack stresses your horse out too much, grabbing a handfull of the loose skin at his neck/shoulders and squeezing (which will pinch really hard by our standards, but in fact is less painful than an /actual/ horse bite.) Obviously not suitable if you have very long nails.
-NEVER smack a horse on the legs, back (spinal area), and your hand ( or in extreme cases, riding crop ) is enough! There should be no need to resort to broom handles or other heavy/solid objects.
-Remember! You are the horses pseudo-Alpha mare/stallion, and therefore should be respected as such!