With some people, we wrap in fabric squares which (a) fight a little less than some papers, and (b) fabric! With the right people, we can see if they want to keep the fabric or toss it back to the original giver for her/his own purposes.

I also like plastic fridge dishes of food with no overwrap. Reusable and less entangling than Saran wrap can be. Maybe a festive stick-on bow. Maybe. I can actually do plausible wrapping, or maybe I should say I used to do, since I don't think I've done any in a while.