Many local shelters have foster programs that allow you to be a Foster Parent to a dog, cat, bunny, or even Guinea pig.
My understanding of how these programs work is that you register with the shelter and when they have an animal come in that matches your parameters (size, breed, temperament, etc), they call you to come pick up your house guest. I also know some rescue groups (breed specific) look for foster parents for the animals they are working to place. Many times, fostering is the beginning of growing your family, after all, some of those babies are just too darn precious to let go of! Dave would never let me foster Cocker Spaniels, I would never let them leave!
This is a great way to help our furry friends and do it on a more temporary basis in terms of time and long term commitment. You can always say no if the time is not right for your schedule.