I am working in Illustrator (15.0.2 (CS5) or 16.0.0 (CS6)) and when I try to move objects small distances, they snap to the nearest two pixels on some invisible grid. I can’t find anything in the preferences. Here are some screen shots:
For new objects, turn off “Align to Pixel Grid” on the Transform panel.
For existing objects, select them first, then turn off Align to Pixel Grid using the checkbox at bottom of Transform panel.