Has anyone gotten useful data from the accelerometer?

[KenWittlief]

you need to step back a bit and look at the big picture. If there is noise and bumps they will be random and will average themselves out over time.

You could also filter the analog signal in HW or in the code. At any given instant the velocity integration may be a little off, but if you are reading it on every loop through your code, and using it for some purpose (like a PID closed loop speed control) the inertia of the motors and the robot will also help smooth out any random noise on the signals.