I've had good luck with 3M products. I bought sets of tiny plastic hooks designed to hold Christmas light wires in place. I didn't use the hooks but did use the double-sided adhesive strips that came with the hooks. They also have the benefit of being removable. The hard part is having the patience to press and hold everything until the adhesive firms up and can take the weight of whatever you're sticking. If you let go too soon, things tend to fall down.
I think they also sell the adhesive tabs by themselves without hooks.