This should be a sticky thread.
You can put bettas in with ghost shrimp, snails, ADFs and a few other fish but it really depends on the size of your tank and the temperment of your betta or the other fish you're thinking of putting in with him/her.
Personally, I've only had one ghost shrimp in with my betta Ludwig in his 1 gallon tank. They got along fine for the few days my ghost shrimp lived after bringing him home.