For those in the New York area, I recommend the Feathered Friends bird sanctuary. For those beyond NYC, there are many good agencies that can help you, including Adopt-A-Pet (formerly 1-800-Save-A-Pet), which functions as a clearinghouse designed to match birds put out for adoption with prospective human adopters. Using Adopt-A-Pet is easy; just select your pet type, type in your zip code with a travel range, and search. When I searched Adopt-A-Pet today, there were many parrots looking for nice people to care for them.
Another good service is PetFinder.com. Again, just type in the kind of animal you're looking for, your zip code plus travel range, and you should instantly get results. So please use a service of this kind if you're looking for a companion and are prepared to make the commitment.