That's right, I'm doing one of these on TV Week. It's easy! Do you know how many shows have riffed on Capra? Loads!
Star Trek: The Next Generation - "Tapestry"
Based on: The story Picard tells Wesley to pass the time on a shuttle in "Samaritan Snare"
The true history: When Picard was fresh out of the Academy, he recklessly tried to cheat a Nausicaan at dom-jot and got a knife through the heart for his trouble. Decades later, he's mellowed and has a mechanical heart he has to get rotated every few thousand miles.
Turning point: What if Young Picard was just a little more level-headed?
Story type: You're lame but the universe doesn't care.
Watcher's mood: Randy.Altered history: A Picard that never had a brush with death might still have a heart, but he might not have a career! Not knowing to live every day like his last, this Picard played it safe and didn't seize the same opportunities, didn't lead an away team on Milika III to save an ambassador, never took charge of the Stargazer's bridge when its captain was killed. So he wasn't offered a command, and never got noticed. Somehow is still winds up on the Enterprise, as a lieutenant junior grade in Astrophysics.
He's under the command of Captain Thomas Halloway who apparently chose the same exact bridge crew he did. (In non-canon material, Halloway oversaw the building of the Enterprise, but retired before he took command of her.)
Stuff canceled as a result: Since Q did say no one else would be changed (tell that to Halloway, the poor man's unable to retire), Next Gen would probably have gone ahead. However, without Picard becoming Locutus, we probably wouldn't have the same Deep Space 9 (not about the same Sisko, at any rate), and without First Contact, the TNG franchise would have ended sooner.
These things happen: On every other show, in fact. Other television episodes that did It's a Wonderful Life include...
-Enterprise's "Twilight" - What if Archer couldn't beat the Xindi?
-Xena Princess Warrior's "Remember Nothing" - What if Xena had never been born?
-Quantum Leap's "A Leap for Lisa" - What if Al died before he could meet Sam?
-Star Trek: The Next Generation's "Tapestry" -
-Married with Children - What if Al Bundy didn't exist and the world was better for it?
-Buffy the Vampire Slayer's "The Wish" - What if Buffy had never come to Sunnydale?
-That 70s Show - What if Eric and Donna had never been together?
-Smallville's "Apocalypse" - What if Kal-El never came to Earth?
-Doctor Who's "Turn Left" - What if the Doctor never met Donna Noble?
-The Simpsons - What if Homer hadn't married Marge?
...and plenty more... Any favorites?