Back in my day we didn't have post-credits scenes. I mean, we did, but they were rare and almost always a joke. Airplane! has a great one, for instance. And the Cannonball Run movies had wonderful outtakes during the credits.
Today it's a different beast. Ever since Nick Fury showed up in the credits of Iron Man (something that was kept secret to the extent that scene was not attached to prints shown to the press), the post-credits stinger has become de rigeur for genre blockbusters. Will your movie have a sequel or a spin-off? Audiences have been trained to sit through the credits and see your tease of said sequel or spin-off.
And that's great.
Matt Singer at The Dissolve thinks otherwise. He finds that they make viewers dissatisfied, "as if they’d paid $15 to see a feature-length trailer for a much-better movie that is always just over the horizon." He points to X-Men: Days of Future Past's absolutely incomprehensible stinger as an example of something that turns theater lobbies into "the sites of impromptu geek lectures, where comic fans hold court while decrypting otherwise incoherent cookies and stingers."
And that's bad?
Not for me. I like when I come out of a movie and I see a crowd standing around talking about what they just saw, not simply rushing to the parking validation machine. You go to the movies because it's a communal experience, and communing afterwards is part of the point. Those conversations, where the post-credits scenes are decoded, often turn into general conversations about the movies themselves, which is nice to see as well.
And what's wrong with asking the audience to do a little heavy lifting? I enjoy writing about the post-credits stingers because I enjoy the research that sometimes comes with it; doing a quick Google search when you get home never killed anybody. The experience of the movie lives on when you get home, if in only a small way.
There's one other wonky reason why I like post-credits stingers: they make people sit through the credits. A lot of people worked hard on the movie you just watched, and sometimes it's cool to take a moment to see their names, even if it is to make fun of how weird they are. There's nothing more instructive than sitting through a blockbuster and realizing the names of Indian or Chinese programmers far outnumber those of the actors and above-the-line creatives. By a magnitude.
As a moviegoer I just like them. I like the tease. The blockbuster is, for better or worse, a serialized experience, and I'm glad that the studios have stopped pretending otherwise. Having a planned story means having a story, which puts these serialized blockbusters one step ahead of stuff like the Transformers movies, which stumble forward two hours at a time. But they're also reaching into the sense of mythology that can surround the best franchises, whether that means referencing a comic book character or bringing us back around to The Fast and the Furious: Tokyo Drift. Not having a planned story is how you end up with Captain Kirk beginning both Star Trek and Star Trek: Into Darkness in the exact same place and re-doing his arc.
The best part about the post-credits stinger? I can just leave. These clues could be in the body of the film - see Batman getting that Joker card at the end of Batman Begins - and that would be fine as well, but by having them in the credits (or after) the filmmakers are letting me know I don't need to see this stuff. It's gravy, not meat. These teases are just that - teases. There hasn't been a post-credits stinger yet that feels absolutely essential to seeing the next film. Which means if you don't like them, don't watch them. You won't be missing out on anything.