The first target of choice is that pesky Apophis, which now hangs like a sword of Damocles - though it is not massive enough to be in the dinosaur-killer category.
Here are some of the Earth protection strategies that are on the table:
Hot Spot: Use a space mirror or laser to heat the surface and boil off material that acts as a small jet and reroutes the asteroid.
Gravity Tractor: Fly in formation with the asteroid for a long period and the gravitational attraction between the two bodies induces a small force that deflects the asteroid.
Asteroid Tug: Rendezvous with the object, make physical contact, and give it a nudge.
Photon Pressure: Make one side of the asteroid jet black or snow white (perhaps using reflectors) the extra absorption or reflection of sunlight will impart a net change of photon pressure on the object, altering its trajectory.
The Home Depot Solution
Physicist Daniele Farigon of the University of Rome has a bold proposal straight out of an Arthur C. Clarke science fiction novel. She suggests landing multiple nuclear powered "mass-driver" rocket motors onto an asteroid's surface. Like a drywall toggle screw, these devices would burrow into the asteroid's surface until they are rigidly anchored. They would then in unison eject mass, like a rocket exhaust, and thereby alter the object's trajectory.