What books/movies/TV shows include finding an infant or toddler as a catalyst for great change for the finder and maybe even their greater community?
I’d prefer fantasy to real life or horror settings, so more like Taran or Hellboy thanMoses or Damien, or but I won’t turn my nose up at those kinds of stories either. What you got?
Willow!
Peach Boy, Momotaro
Does Paris, son of Priam of Troy, count? He wasn’t exactly “found”, he was “re-found” by the herdsman who exposed him on Mount Ida and was very surprised to run across the baby still alive and thriving* a few days later.
*Suckled by a bear, in case you were wondering.
Superman?
And somebody’s gotta say Moses sometime, so I’ll do it.
Moses.
You mean other than the OP? 
How about Harry Potter?
Barbara Kingsolver’s book “The Bean Trees.” A single woman finds an abandoned, abused toddler.
Oh yeah. Totally missed that.
As for Harry Potter, ISTM that wasn’t so much “finding a foundling” as a very hastily arranged intra-family adoption.
*The Last Unicorn *by Peter Beagle has, among many other things, an abandoned child on a freezing night being kept warm by a blanket of cats. He proves to be the catalyst of great change for the community.
In David Eddings’ Belgariad series, the evil sorcerer Zedar adopts a street urchin named Eriond who’s instrumental in stealing the Orb of Aldur, which pretty much kicks off the whole second half of the series. In the sequel series (The Malloreon), Eriond ultimately becomes a God.
More down-to-earth, in the film The Impossible, the mother and her teenage son help rescue a six-year-old boy while they themselves are desperately seeking shelter. However, the only effect of their actions is that the kid doesn’t die of exposure (which I suppose is pretty important to the kid & his family.)
The animated movie Ice Age (I think number one) - the animals find and protect a human baby and journey to return the child to the humans.
Elvenbane and sequels. The dragons raising Shana after her mother dies in childbirth is the catalyst that sets off the entire series.
THE THREE STOOGES movie (2012)…
Snow White
Everything Is Illuminated
A nitpicky note for people considering reading - the Halfblood Chronicles is unfinished, and as far as anyone can tell, will remain unfinished. If that bothers people, it’s better to know beforehand, because they are very enjoyable books that all set up to a final volume - that doesn’t exist.
Popeye.
Children of Men
No mention of ***Silas Marner ***yet?
Or Oedipus Rex?
Disney’s version of Hercules?
Shakespeare’s ***The Winter’s Tale ***?