The shelter I adopted both my cats at (and now volunteer taking care of the dogs at) works like this;
Cats are $150, kittens under 6 months are $175
Dogs are $250, puppies under 6 months are $300
Older animals often have their fees reduced, or even waived. They also sometimes do 'better with a buddy' promotions for cats where when you buy 2 cats together one is free or half off or something like that.
They also have a great palliative care program for elderly pets. Basically the shelter provides everything for you (including food and medical care) for the duration of the animal's life. 'You just provide the love' is what they tell people.
For cats, you fill out an application and show driver's license as ID. For one of my cats they provided medicine for her URI, which cleared up quickly once I got her home.
Dogs are required to meet everyone who lives in the household (even if it wont be 'their' dog) as well as any other dogs already in the home. For puppies and some adult dogs with specific behaviour issues you have to have pre-enrolled them in a puppy or obediance class and show proof before you can adopt them. They give the option of having the dog microchipped for $20.
All animals are up to date with all their vet work (shots, worming, etc) and spayed or neutered before going home. You get a package with all their medical info, as well as a free visit to a vet within 48 hours to make sure everything is okay. If the vet prescribes anything for them, the shelter will fill the perscription for you for free.
We are -very- lucky in that our shelter is partnered with Iams, and Iams provides all the food the shelter needs free of charge (in exchange for putting their brand on things, basically). Normally the pet will go home with at least half a bag of food, provided they food they need (kitten vs cat, etc) is available at the shelter.
After reading about all of these bad shelters, it makes me really appreciate how well ours is doing, and how lucky we are!