Only twice did I go out of my way to save baby animals. Once was a bird which my cat, the huntress, Callie, was playing with. I got the kitty of its poor tail feathers and it was uninjured, though a little shocked. I carefully cupped it and put it back in the tree with its nest, and considering I didn't see any baby bird presents that year, I think it survived.
The other time was at elementary school, and saw an obviously injured bird (broken wing), so I cupped it in my hands and took it to the office, who called I think the BLM over to handle it.
I think, one of the funniest times I've ever dealt with baby birds, is when my poor, couldn't hunt to save his soul, cat Andy (Callie's brother) was getting divebombed by some hummingbird. He came out of it scratch free, but when we came home to see his poor plight, he immediately ran to us and looked like "Let me in!"
Yes, I am a softie. But I generally let nature take its course, or let the professionals handle it if its a minor problem. Sometimes, I do get a kick out of feeding pigeons birdseed, but probably because it's far healthier than anything the McDonalds they live outside of has to offer.
Those are some fat pigeons.