You can tell I cheating, but yes, if you take as trajectory a straight line of field. This is the case for the electric field around a charged sphere. Or a little less true for a point placed at high potential. This is how the "atom microscope" works.
This depends a bit on what sort of nonuniform electric field you're talking about. If the field has a non-zero curl, then most likely not. But as Lpfr said, the charged sphere electric field allows rectilinear motion, as do many others.