All kinds! Basically any kind of animal you can buy or adopt, may need a foster home when they lose their home. Of course, the biggest need is cats and dogs.
Sometimes there are orphaned kittens that need to be bottle fed, or injured animals that need special care. Sometimes there are pregnant mommies, and care is needed for the puppies/kittens and the mom until they are old enough to be split up and go to separate fosters.
No matter what kind of room you have in your home, you can help.
Special help is always needed for the breeds of animals that are overbred and highly disposable. These breeds, such as pit bull mixes, are always in need of fosters and are hardest to place. Not because they are bad dogs, but because of the social stigmas that limits the number of people comfortable fostering and adopting them. If you are serious about helping and making a difference, I encourage you to do some research on the pit bull mixes, and more importantly, get out and meet some at adoption events and consider fostering them. Advocates are needed for this wonderful, misunderstood breed. And of course, fosters are so desperately needed!