This is a fantastic way to find lots of great volunteer opportunities with the National Parks Service, the US Fish and Wildlife Service, the USGS, and lots of local agencies. Help hatch trout in West Virginia, monitor birds' nests in Ohio, tend a butterfly garden in Iowa, or be a Seabird Docent on Alcatraz Island-- the list goes on and on!
Servnet.org is a great place-- for young people especially-- to find volunteer opportunities (and events) posted by local nonprofits. You search based on location, "Causes Served" (check the "Animals" box) and your "Volunteer Age Range".
Idealist.org is a fantastic site for finding opportunities to dive in and make a difference! They have a good set of listings for people living in different parts of the world, too. To find volunteer opportunities helping animals, scroll down to Wildlife and Animal Welfare under Area of Focus.
This is one good way to find opportunities to volunteer to help animals, especially for young people. Check "I want to volunteer", enter your zip code, type "Animals" into the keyword box and, if it applies, check off "Kids welcome" or "Teens welcome" and voila!
If you want to volunteer at a local shelter, you can fill out some data about yourself and register on this Petfinder page, then "shelters and animal rescue groups in your area can search for people like you wanting to make a difference in the plight of homeless pets in your community!"