As one of the kennel technicians at Tri-Lakes Humane Society, I can tell you, this is one of my absolute favorite activities to do with the animals! I've found that it helps especially with the shyer cats and dogs as well as feral kitten groups that we've gotten in. I myself have found that reading to the shelter pets relaxes myself so much that I've taken up reading to my own pets at home!
There are many benefits to reading to shelter pets, not only for the pets, but for the readers as well! Reading to the pets that are housed in shelters help them become more relaxed and socialized which usually helps them get adopted quicker. Young readers gain more confidence by reading to pets because they don't judge your reading skills. This also helps new readers become more motivated to keep practicing their reading. The shelter pets are happy with the one-on-one interaction that they get and the soothing effect from the calm voices reading to them. Adults who read to shelter pets also find that it's not only calming for the animals but calming for them as well.
If this sounds like something you might be interested in doing, I encourage you to check out your local animal shelters and libraries to see what kind of volunteer opportunities and reading programs they have!