I volunteer at an animal shelter. I enjoy walking and playing with the dogs and cats, who are generally very lonely and LOVE to be given affection and taken outside where they are out of their cages.
In my experience though, animal shelters need the most help with doing the dirty work -- like laundry (washing toys, blankets, etc), cleaning out dog bowls and litter pans, and cleaning cages. That's less fun of course, but rewarding knowing you are helping the shelter which helps the animals.
When I go, I generally do whatever the workers need from me for about an hour (usually they ask me to do laundry), then I play with the dogs and cats for an hour. It's a perfect way to spend my Saturdays