As Ram said, it depends on the type of bird. When I adopted my cockatiel, he was actually houses with doves, and they got along fine. I know of some people who house cockatiels and budgies together and they do okay, but others say the budgies bully the cockatiels, believe it or not! I would personally never house a larger parrot such as an African Grey with a smaller bird. I probably wouldn't risk it with a conure, either. Those large parrot beaks can do a lot of damage to a little budgie.*housed with doves (hate when I find a typo in my post after the editing time limit has expired!)
Anyway, I just thought I'd add - I had my cockatiel in at the vet's office for a nail trim, and a man in the waiting room with an African Grey told me that he's heard of African Greys actually biting off the beaks or legs of smaller birds, so please don't put a Grey in the same cage as your budgies!
