Decent latches and padlocks on everything. Bicycle cable locks can also be useful if you can't use a hasp but can fit a couple of eyelets across a door/lid. One set of bike locks is padlocked to the eyelets, another is threaded through.
I've had more problems with people than eg foxes. Had a couple of rabbits stolen from different runs one Sat afternoon - worst feeling ever. Got them back a couple of days later as they were about to be dumped - mainly due to putting posters up everywhere. I never want to go through that again. Nothing will stop someone with bolt cutters, though.