For the most part, Doctor Strange works because it tells a story independent from the rest of the Marvel Cinematic Universe. It's a by-the-numbers origin story for the titular hero, and an avenue for psychedelic new possibilities in Marvel's multiverse (which also makes for mind-bending and entertaining as hell action sequences).
But that shouldn't be misinterpreted as a story that doesn't still tie into the rest of the MCU.
(Editor's note: Spoilers for Doctor Strange ahead.)
The big connection that Doctor Strange provides is in the form of the Eye of Agamotto, the amulet Strange uses in the film's third act to defeat Kaecilius and, by extension, Dormammu. As Wong reveals after the conclusion of the fight, Strange was using an Infinity Stone.
This was the Time Gem that — as the name suggests — manipulates time and space. To give an idea of what that would be like, Marvel aired a Doctor Strange teaser that runs backwards, akin to Strange using the Time Gem to stop Kaecilius from destroying Hong Kong.
More importantly, this is another on-screen instance of an Infinity Stone being used, similar to the ones featured in The Avengers, Captain America, Guardians of the Galaxy and Thor: The Dark World. Where's all this leading to? A pretty intense matchup with Thanos, a purple-ish, weirdly CGI'd Titan seen briefly in Guardians and Marvel end-credit scenes.
He owns the Infinity Gauntlet, and if and when he gathers all the Infinity Stones, he will be nigh impossible to defeat. That is, barring something unexpected, where we're headed in the next Avengers film: Infinity War (it's in the damn name, after all).
Infinity War should feature every Marvel hero under the sun, and if Thanos means to capture all the Infinity Stones, that should include Strange and the Eye of Agamotto. Plus, with whatever havoc Thanos inevitably wreaks on Earth, moving back time to fix some of the damage would actually be very useful.
We've still got a few Marvel movies in the MCU timeline before we get to Infinity War, but expect Strange to make an appearance then. If that's too long of a wait for some Benedict Cumberaction, the hero should also be in next year's Thor: Ragnarok.