The manga averts the trope. In the Distant Finale, it's revealed that after several years of maintaining their relationship long-distance, Syaoran completes the paperwork to move to Japan on a permanent basis, making it more of a happily ever after ending.
Another CLAMP example, Chobits ended with all of the servitor robots, or "persocoms" developing sentience. How humanity responds to this isn't dealt with. This didn't happen in the manga though.
Martian Successor Nadesico. The end of the series simply dropped multiple plot threads all over the genre board, from sci-fi to political to romantic, and ended with the main couple suddenly coming to terms with their undying love for each other in the last ten minutes. Ruri even lists the abandoned threads and then assure the viewer, "but we're not going to deal with them right now." The hanging ends, unfortunately, were ideal material for the Darker and EdgierMovie, which it abandoned for more Ruri.
Ranma ˝ ended with Ranma and Akane running to school together. It is implied that Ranma and Akane will eventually get together. How they're supposed to do that, though, is something Rumiko Takahashi wasn't interested in showing (probably because, when asked, she explicitly stated that Ranma and Akane were the only true couple in the series...)
Watchmen arguably ends this way: although The Reveal (actually a series of revelations) resolved a whole lot of plot points, Dr. Manhattan, who's in a position to know this kind of thing, claims that nothing ever really ends. The Dénouement apparently bears out his claim: the world is now just barely politically stabilized under a fragile peace accord that may or may not last, the costumed vigilantes Dan Dreiberg and Laurie Juspeczyk are still at large and plying their trade under new identities for how much longer no one can be sure, and a certain journal that a very minor character may or may not be about to discover may or may not ultimately blow the lid off the huge secret these costumed vigilantes are keeping from the rest of the world. It's deliberately left up to the reader to speculate what's going to happen next.
While the first Hellboy movie ended normally, the second finished with the entirety of the non-normal BPRD quitting and Liz revealing she was actually pregnant with twins. No clue how a half-demon, a pyrokinetic, and an icthyosapien are going to lead "normal lives" or what Krauss is going to be doing. Apparently del Toro had intentions for a sequel to the sequel, however, so he may just be leaving it open.
At the end of the movie The Graduate, after Benjamin rescues Elaine from her wedding and they flee on a bus, the camera holds on them for an uncomfortably long time, emphasizing the "now what?" nature of the ending.
A play and a (separate) movie attempt to tell what happened right after the end and a generation later, respectively.
By midway through the 2008 Iron Man movie, Tony Stark has a portable clean energy source which could completely revolutionize global society, plus an AI which could pass the Turing Test if it cared to try. The scene after the end credits strongly implied that the next movie will feature him and Samuel L. Jackson beating people up.
This is finally dealt with in The Avengers, in which Iron Man's arc opens with Stark finally putting the finishing touches on a revolutionary clean energy generator. Though it is not directly stated, it's implied that the worldwide response to this was enormous. The development at least caused enough waves that that the Big Bad (who is not only from space but spends most of his planning stage in a bunker somewhere cut off from the rest of the world) heard about it enough to make comments and incorporate it into his plans.
Tony wants to put more research into the larger arc reactors which could be used as power plants, but the miniaturized reactor is so easily applicable to weapons technology that Tony won't risk selling it. The sequel shows that this is completely justified. Also, the Iron Man movies do indeed avert Reed Richards Is Useless. Technology in general in the Marvel Movie Universe is quite a bit more advanced thanks to the nigh superhuman genius of Tony and his father and, to give credit where credit is due, Vanko.
The ending of THX-1138. The title character manages to escape the underground city, and the ending has him standing in the middle of what appears to be an empty wasteland.
Melody(1971) ends with Daniel Latimer and Melody Perkins escaping from the adults' raid on their wedding and cranking themselves down the railroad track on a trolley. However, this "man" and his "wife" are only ten years old! No government is going to recognize their marriage legally. They barely even know anything about kissing, let alone sex. So what kind of honeymoon are they going to have? Good question.
The Candidate...Naive lawyer learns how hard it is to win, and learns about the machine. "Marvin ... What do we do now?"
A very positive example, 50/50 ends with this exact line — a tremendous relief that it can even be asked after having just survived cancer.
The Buffy the Vampire Slayer finale played this one perfectly straight. In the last scene, Xander lays it all out for Buffy: the Hellmouth is closed forever and Buffy isn't special any more, doesn't have any destiny... so now what? The last shot of the series is Buffy starting to grin as she realizes that for maybe the first time since she picked up a stake, the answer to that is totally up to her.
And of course, the question was answered in the Season Eight comics.
In Battlestar Galactica, when Baltar is found not guilty of treason against humanity, he is basically now alone in the universe; he doesn't get to go back to his cell (he's no longer a prisoner), he will probably never be trusted again (by the Colonials), and he has no want (or desire) to contact the Cylon fleet (which would probably be considered another act of treason.) Luckily for him, the womens' "church" of the one God show up out of nowhere.
In House, the season 6 ending has House and Cuddy admitting they had romantic feelings for each other; the season 7 opener, titled "Now What?", shows their attempts to make a relationship work.
The War of the Worlds: Hoorah, we've defeated the Martian invasion! That's the last we'll see of them! Well, until they invent disinfectant, anyway.
Answered in an unauthorized sequel, Thomas Edison Conquers Mars
Several of the Discworld books have this, perhaps most notably Interesting Times and Going Postal, possibly due to the fact that the central characters were semi-nomadic in their lifestyles but are now stuck in positions of authority.
KOTOR II was supposed to end with the main cast flying away from Malachor V in the Ebon Hawk. Atton would then ask the Exile "So...where're we going now?"
At the end of Portal 2, Chell, and her Weighted Companion Cube, are finally released from the facility by GLaDOS. The only problem? It's several hundred years in the future, there's no sign of humanity, and the Combine might still be around. The fact that she's a Heroic Mime won't help much, either.
The "Art Therapy" DLC at least reveals there are other humans out there.
Yuriko's campaign in Command & Conquer: Red Alert 3 - Uprising ends with Yuriko killing Izumi in self-defense, then flying out of the facility, landing on a hilltop, and wondering what to do next.
In Klonoa 2: Lunatea's Veil, it's strongly hinted that Klonoa has divine blood and that his forced wanderings are serving some greater purpose. The game ends just as he's being drawn out of Lunatea. Namco never released another Klonoa game.
Ultima IV is entirely made of this trope. See, in all previous Ultima games, you defeated supreme evil...and now there are no more bad guys to fight aside from random monsters in dungeons. What's your goal? To become a Messiah!
Batman: Arkham City ends on this note. Batman simply leaves the city carrying The Joker's poisoned corpse out with him, leaving a crowd of prisoners, citizens, and GCPD members alike to wonder exactly what happened in the city during the past twelve hours.
Gargoyles ended this way (if one accepts the Nelvana season).
The picture at top is from the 1980 Road Runner cartoon "Soup or Sonic". Wile E. Coyote has as long last managed to get his grimy paws on the Road Runner. Trouble is, the last gag of the cartoon left Wile E. inches tall vs. a normal-sized Road Runner. So he plays the trope with his usual Talking with Signs. The cartoon ends at that point, leaving any answers to the viewer's imagination.
A more serious case, at the end of the Transformers Prime film "Predacons Rising" once Megatron has been freed from Unicrons control, he comes to the realization that he's now totally alone in the universe; he doesn't stay on Cybertron (he knows he'd probably no longer be welcome), and he no longer has any desire to lead the Decpeticons in conquest (he goes so far as to officially disband the group).