What's an easy & inexpensive way to cover a milk crate?

You could sew a fabric cover.

why not just re-paint them

I would sew (or glue and velcro) covers for them. I like fabric as when they get dirty or dusty, easily laundered.

Fabric might be an idea.

I third the two suggestions above. A fabric cover could be adorable.

Paint then weave fabric strips. In and out of the holes

fabric covers would work... but if you can't sew... you could weave rope or twine or webbing in and out of the holes (depends on how the crates are made) You could use binder clips, to hold the top of painters canvas (or other heavy fabric) and just wrap like a present....use grommets hold the sides or glue on velcro (the self-stick kind won't wash) to hem the edges use a washable glue like Aleene's OK to Wash It.

Thank you all so much for the feedback, great ideas!