I know that it’s a banning offense to link to TV Tropes, but … Happily Adopted.
Nobody has mentioned the Bible? Jesus, Mary & Joseph!
I seem to recall hearing about—although Google isn’t turning up any primary sources, at the moment. 
—an old Arab fairy tale/folktale about a girl who was adopted by a Ghoul, who not only was a loving parent, but granted her some of his powers.
I didn’t notice this thread was a zombie at first, then I saw that someone had beaten me to mentioning Momotaro by more than a year!
There’s another famous Japanese fairy tale, “The Tale of the Bamboo Cutter”, that also involves an elderly couple finding and adopting a baby – in this case a baby girl found inside a stalk of bamboo.
I see what you did there. Great username-post combo, too.
I find it odd that this is considered a trope, since in my experience, it’s typical: adoptive parents are deeply grateful to have children, and the children are cherished. I’m adopted, as is my son, my brother and sister, and a number of friends. I even have a friend who was adopted and has a natural-born sister of the same age. (I learned that this isn’t unusual: once an adoption is more or less assured, tension releases, and fertility rises.)
I only know of one case where things weren’t nearly story-book. A close high-school friend was the child of a single mother who married a man who adopted him at age three, and they then had two more children. He felt he was treated differently from the other kids by the father. He found out the truth practically in the middle of an argument. It’s understandable that he had issues. IMHO, that scenario is more of a TV trope than the happily adopted one.
I also find it odd that I can’t find a TV trope for the evil adoption agency, which tries to force unwed mothers to abandon their babies, the agent usually played by a wicked looking person, either a harridan or the evil-banker looking type. I’ve seen that one so many times it makes my eyes roll.
I’ve never seen that trope on TV or in movies, but there’s a very common trope in which nice people adopt a baby, raise it for years, and then lose it when the birth mother comes back seeking to regain custody.
I’m not saying that never happens, merely that it’s very unusual.
Terry Pratchett handles adoption nicely in several instances:
Carrot Ironfounderson is a human adopted by Dwarves. They raise him well–as a Dwarf!–and he turns out great.
Death (the anthropomorphic personification) adopts a daughter, who marries his assistant Mort, and they have a daughter, Susan–“Death’s adopted granddaughter,” who also turns out great.
I know there’s a 3rd example but it’s not springing to mind immediately.
Most of the entries on TV Tropes are for things that are typical, or at least fairly common, in fiction. (It’s not a cite about tropes you don’t see on television.) Some of these entries are also things that are fairly common in real life; these are known as “Truth in Television” and the Happily Adopted article is noted as such.
As both a step-parent and bio parent myself, I would say that step parents get a bad rap. Most are loving, warm and compassionate people who have opened their hearts and home to their stepkids… They often get all the difficulty of a bio parent, with none of the ‘wins’ …but I digress.
The father in Will Farrel’s Elf is a great step dad.
You may also enjoy this Brad Paisley song about a loving stepdad, “He Didn’t Have To Be”:
Most are common in a particular section of fiction, but I wouldn’t say most are common in all fiction. They have the whole PeopleSitOnChairs exception, after all.
Being happily adopted is only a trope if it has meaning to the narrative, and I’d argue it usually does not. Being unhappily adopted, on the other hand, always has meaning to the narrative.
Then again, the site stopped being just about “tropes” a long time ago.
There is a good stepmother (always called “Mom”) in Doris Gates’ novel Blue Willow, and good adoptive and foster parents in her novel Sensible Kate.
YMMV. My real-life ones have always been assholes and bitches of the highest order and I have had several. I always cheer when a step-parent (almost always the step-mother) gets killed or brutalized in a fairy-tale. That is a big part of their appeal to me at least.
I promised my daughters that they will never get a stepmother mainly because I would never, ever consider doing something like that to my flesh and blood but also because I don’t want to end up on an episode of COPS after the inevitable conflicts occur. My motto is flesh and blood over everything.
Another good fictional stepmother: Kate in Louise Fitzhugh’s Sport.
I’d forgotten about this thread, and I haven’t been checking Cafe Society that much recently, so this was really cool to see! I would love to see more!
Shagnasty: hi Dad! …my dad’s family features an evil stepmother (only one, though), which has, sort of grimly-hilariously, made them super worried about my step-uncle-by-marriage remarrying after the death of his wife (my step-grandmother’s daughter).
I highly suggest Book of Lost Things, which is one of my most favorite modern fairytales. The boy protagonist gets a stepmother that tries to be decent but he is a total brat to her (although to be fair he is still grieving his mother’s death).
Closest I can come is Joe Gargery from Great Expectations.