Almost certainly a grounding problem, or a crosstalk problem. Had that myself when I first fired things up.
Make sure your power supply has a good ground setup. I found at one point I was getting a 48 V ac sine wave on my grounds, due to a difference between the laptop's USB ground and the ground on the Reprap power supply. Grounding the chassis on my laptop fixed it for me. Set your multimeter to AC Volts and poke around your grounds while everything is fired up.
For crosstalk, watch your wire routing. Any noise on the "step" wire to the driver board is probably being interpreted as a step command. Make sure you're running the stepper motor wires as far away from the control wires as possible. If they have to cross, try to do it at 90 deg angles. Using shielded, grounded cable can help too.
I'm not sure about your electonics layout, but this is one place where distributing the driver boards on the Reprap frame can help a lot - it keeps the noisy motor wires short and away from the control wires.
Hope that helps!
Wade