I've rented many years yet love pictures on my walls. Command 3m hooks have been a godsend: reliable & completely removable. Just be sure to pay attention to the weight of your picture, and match it to the right hook. That is very important. If in doubt, use two hooks side by side to share the load. And clean before sticking, with isopropyl alcohol. I've found they are great too when you change your mind or just want to freshen a room by moving pictures around/changing them out. No guilts about holes! &hooks are reusable. They aren't as cheap as some removable hooks, but for me they've been worth the investment! :) :)

I do it anyway, we just carefully spackle and paint before we move. Honestly, I'd get a new landlord!