Sealed Cables

Brake and deraileur cables can pull mud into the cable sheath as the wire slides back and forth. One option oft suggested for waterproofing is to dab some silicone at the ends of the plastic sheath, at the point that the wire emerges. The water-proof silicone will seal the braze-on and the inside of the cable housing to some extent, reducing the friction created by grit and corrosion.

A more deluxe option would be to use an inch or two of plastic tubing, such as a thin surgical tube or heat-shrink tubing. Cut the tube down the side and wrap it over the cable where the cable housing ends. To seal the cable just before it attaches to the brakes, remove the cable from the brake mechanism and slide the tube up, intact.

With V brakes, little black rubber acordion tube things called "mud boots" are available, specially designed to keep the guck out. They slide over the cable at the top of the V, sealing the cable in large part as it sliders through the mud boot. These can be mounted on cantilever brakes as well, in much the same manner as the thin surgical tube above.

Anchored Grips

Thin safety wire, wrapped tightly into grooves at both ends, can be used to anchor the grips and to seal the inside from water. You may have to carve the grooves in, if your grip pattern doesn't support this. Wet or muddy grips will otherwise twist and slide about as you ride, making it impossible to torque on the handlebars with the wrists, and for those without bar ends, opening the distinct possibility of the grips sliding right off the bars in the middle of a ride. With some grips you won't experience any sliding, so only do this if you've had previous problems.
Corn Oil

Spray non-stick corn oil on your down tube to keep the mud from sticking as your tire kicks it up. From experience, I would use it on my seat post, down tube, seat tube and possibly rear triangle. Make sure you don't put it anywhere that you might touch with your hands, as your grips will become slippery. Keep in mind you will have to clean your bike off anyway, it will just be easier!

The Wonders of Judy Butter

To lubricate and displace mud, use judy butter. (You can also try nonstick corn oil as above, a cheap alternative to Rockshox super expensive butter.) If your pedals get packed with mud to the point that they don't work smoothly, pack both sides with judy butter in advance. The action will remain smooth with the soft grease in place, and when you biff and slam the pedal into a patch of mud, the pedals will continue to work smoothly. Otherwise, most inexpensive pedals will refuse to release your foot without minutes of coaxing.

When experienced riders go out mud bogging, they will often replace the ordinary light chain lube oil with judy butter or parafin wax. This will help to prevent dirt and grime from clogging up and your chain and cogs.

Deraileur Hoods

Most bike stores stock little rubber hoods for the front deraileur. These are nifty little inventions which work quite well in shielding the mechanism from mud. These are a great alternative to having a solid block of mud for a front deraileur.
Drain Holes

Clear the drain holes in your rear triangle and bottom bracket and on some bikes on the fork as well. This will allow water to drain out of the frame, preventing rust, and reducing the weight. Also check your dust caps and handle bar caps. If you ride in the mud without handlebar plugs, they'll be plugged up for good.

Fenders

On mountain bikes, full, close fenders are terrible because they collect debris and jamb into the tire. On touring and road bikes with slick tires, debris won't be kicked up so fenders are more effective. Some models are more effective than others, but if you are out mud bogging or in the rain, don't bother. While there are lightweight and durable fenders designed for off-road riding, if they are to have enough clearance they won't work as effectively. In my experience you will get covered no matter what, however, i've had reports from people who say seat post mounted fenders can keep you from looking like an inverse skunk. I still don't see how it can help your time, but if your worried about how you look you might want to try a Zefal Flamingo seat post mounted fender.