Gophers are vegetarians, but that's far from a benign characteristic as far as your plants are concerned. Most of the gophers North Americans are likely to encounter are pocket gophers -- the pockets being two oral pouches in which the animals carry food. The most reliable way to control gophers is to trap them, but if skewering furry varmints isn't on your to-do list, there are several nonlethal control methods to try.
Take Away Their Food
Weeding your yard can reduce its viability as a gopher habitat because many weeds have the long, fibrous roots that the animals love to chew. Of course, that makes it more likely that they'll go for your prized begonias, but not if you had the foresight to surround the roots with gopher wire when you planted them. If you didn't, consider surrounding your your flowers and vegetables with a semi-rigid plastic barrier that extends 30 inches underground and 6 inches above it. Gophers are poor climbers and will probably tunnel around the barrier rather than try to go over it, and if the rest of the yard is free of roots, they'll leave.
Flood Them Out
Attempting to flood gophers by filling their tunnels with water is a risky proposition; the water can undermine your yard and create drainage problems for your neighbors. You don't have to go to that extreme, though. Simply overwatering your yard -- if you're in a region with ample water -- can make tunnels more difficult for gophers to navigate. As the tunnels fill with water, the animals come to the surface, where the muddy soil sticks to their fur and claws. When they eventually come above ground, they become easy pickings for natural predators.
Get an Owl -- or a Cat
When gophers come to the surface, they become prey for owls, cats, dogs, coyotes and snakes -- especially gopher snakes. Introducing any of these predators is a way to limit the gopher population, but unless you implement some other strategy, such as overwatering, natural predators alone are unlikely to eliminate gophers from your yard. Barn owls are especially effective predators -- you attract them by installing nesting boxes around your yard. Owls range over a large area and remain in places where the hunting is best, though, so they aren't likely to come if you only have one or two gophers. Give the job of eliminating a single gopher to your cat.
Put a Barrier Around Your Yard
If your yard hasn't already been taken over by gophers, you can keep out all but the most persistent ones by burying gopher wire around the perimeter. Use wire wide enough to bury 24 inches deep with a 6-inch, 90-degree bend away from the yard on the bottom to discourage an animal from burrowing underneath it. If gophers come into your yard before you have a chance to install this barrier, spray a dilute solution of castor oil and water on the grass. This has been known to repel gophers temporarily, and hopefully, they'll stay away long enough for you to finish the barrier.