Choose Your Own Nostalgia

So I've been watching Girl Meets World, which is basically a sequel series to Boy Meets World. It veers a little close for comfort at first towards being a "next gen fanfic" (where everyone's basically a xerox copy of their parents), but fortunately it avoids it, and even Maya, who is a bit of a Shawn expy, is very much her own person. I'm not watching the show faithfully, just a few episodes I've heard were good, but it's fun nonetheless.

Here's my question, though - what series did you grow up with do you think could have a plausible continuation, either a "next gen" thing or even the characters as being older? OR, what other series have done this that you enjoy? Spiritual successors don't really count, unless you want to argue that they could very well be in the same universe (that would be interesting, so let's hear it).