-If it's just a puddle, ride in the center of it to minimize the amount 
 of trail damage.
-If it's deep and wet, spin in a low gear and keep seated so that your 
 back end doesn't spin out.
-Try to put less weight in the front.  The front tire might plow into the 
 mud, causing you to endo.
-Pulse both brakes after going through the mud to scrub off the mud.
-Mud, much like water, can do a lot of damage to your bike, so be 
 careful.  Also, it tends to wear out the brake pads very quickly.

Other riders also added:
[rokslyde@sowebo.charm.net]
Try going though thick mud fast, you will sort of "hydroplain" across it 
which leaves less goop in your brakes and gears, this also has the 
added advantage of getting through it quicker.

Dave Blake [dblake@eureka.wbme.jhu.edu]
Do not ride through mud if you have another option - the trails should
come first, except in races.  You cannot overemphasize the importance
of maintaining the trails properly in this day of trail closures.

Brian Adams [adams@cs.unr.edu]
-I've had mud gob onto the rear derailleur; the chain then grabbed it and
 twisted it into junk.

Rik Allen [richard@prl.research.philips.com]
If the mud is short and firmish, stand up tall and stay light on the
pedals, almost hopping over it. "Think light", and skim over the top.
Easier to do than describe. Powering through will bed you down in.

There are many different types of mud, each needing their own
techniques.