I wouldn’t disqualify all in-show pregnancies and such. Sometimes (as was the case on Angel) the newly born has a speaking part rather soon after being born (actually, happened more than once on Angel, though the second time it happened was a LOT more extreme). That said, this hardly spelled the end of the show, as it culminated in a couple of my favorite plot twists (years of watching Babylon 5 and Buffy the Vampire Slayer have taught me to never EVER take a prophecy at face-value.)
Buffy the Vampire Slayer, now that I think about it, introduced the character of Dawn (Buffy’s teenage sister) out of nowhere in the beginning of the 5th season. Her sudden appearance, complete with retroactive memories of her by everyone who knew her, was later explained though.
Babylon 5 does this a couple of times too, but to much lesser degrees. One example is the introduction of Captain Lochley in the 5th season, who later turned out to be the never-before mentioned ex-wife of Captain Sheridan (his first marriage, no less). In this case, it was explained that they “fell madly in love, got married, and a few weeks later fell madly out of love” getting a divorce, an annulment, and apparantly pulling enough strings to get all evidence of the marriage erased to the degree that Garibaldi (a security/intel expert and a sometimes private eye) wasn’t able to find out about it while actively snooping until he just up front asked Lochley about what connections she had with Sheridan.
As it is, this facet of their relationship never really seemed to become relevant beyond the fact that Sheridan wanted to bring in someone to run the station that he could trust and who everyone else in Earthforce could trust (she was one of the officers who didn’t sign on with Sheridan in the Earth Alliance civil war that happened during the 3rd and 4th seasons of the show)
I’m not sure if you could say this led to the demise of the show (apparantly it only ended when it did because the producer refused to do a sixth season, instead opting for the creation of a new spinoff, Crusade. What caused THAT show’s demise in it’s first season is an entirely different can of beans that has nothing to do with this topic.
Now, ever-so-slightly off topic, but still dealing with the introduction of new characters to a show, you have examples like Law and Order, which currently has NONE of it’s original stars, the entire cast having been replaced by new characters over the course of the show (which works for that show’s format, being that it’s a show about the criminal justice system, but not necessarily the people involved in it) I still love ot watch the newer stuff of Law & Order. In fact, I liked the cast as it was before Jerry Orbach died (RIP Detective Brisco). Who did they replace him with on the show? Asking out of curiosity, as I watch it in reruns.