I've written a short example of how to use a Kalman filter to produce a tilt angle estimate from a gyro and accelerometer. tilt.c and tilt.h have comments that explain the techniques used in the filter. If you're building a balancing robot, this is an easy way to avoid buying the expensive Microstrain FAS-G sensor that Dave Anderson used in nBot.

There are lots of other Kalman filters that I have written, but they are not as well documented as the 1 axis version. fast_ahrs.c is a full three axis, nine sensor attitude and heading reference filter hand optimized to run on a small microcontroller. gpsins.cpp is a GPS aided INS with 17 states. AHRS.cpp is an easier to read version of the 7 state AHRS code. All the source code is Free Software under the terms of the GPL.