Half of the Asgardians still live.

Later in the movie, Thor describes Thanos and claims

Thanos already has the Power Stone because he stole it last week, when he decimated Xandar. He stole the Space Stone from me. When he destroyed my ship and slaughtered half my people.

Not all my people, just half.

Joe Russo commented, and also reported in ComicBook:

The director did not say how, but he did say a portion of the Asgardians also survived. Russo said escape pods ferried those survivors away from the battle, giving the Asgardian race the chance to escape extinction.

So yes, there are still Asgardians out there.

Infinity War and Endgame update: Five years after the snap, we see Valkyrie and many Asgardians in the New Asgard. Banner even tells Rocket:

Hey, have a little compassion, pal. First, they've lost Asgard, then half the people. They're probably just happy they have a home.

Best confirmation we can have.

Nothing official, but two Asgardians that are unaccounted for are Lady Sif, who didn't appear in either Thor: Ragnarok or Avengers: Infinity War, and Valkyrie, who was weirdly absent at the beginning of Infinity War, even though she was present at the end of Ragnarok (along with Korg).

According to Jamie Alexander (the actress who plays Sif), it was a scheduling conflict with her show (Blindspot) that kept her out of Ragnarok. If Marvel can work that out, I'd say there's still a chance for her to show up again in the MCU.

Since this question was originally asked, we've seen Valkyrie and many other Asgardians living on Earth in Avengers: Endgame. Half of the Asgardians that survived the destruction of Asgard in Thor: Ragnarok escaped from Thanos and made their way to Midgard (Earth).

We also saw Lady Sif show up in Loki, but it wasn't clear (to me) when in time this version of Sif was from.

Now that Avengers: Endgame is out, we know that some Asgardians survived indeed,

and settled "New Asgard" in Tønsberg, Norway, with Thor as their leader. These Asgardians include Valkyrie, Korg and Miek (Thor's fellow gladiators from Ragnarok). It's unclear how many people were there, but New Asgard overall looked the size of a small fishing city. It's also unclear how they went from the wrecked spaceship in outer space to Earth.

Yes

Joe Russo has now confirmed that Asgardians, including Valkyrie survived.

There certainly were survivors — Thor does say to the Guardians that [Thanos] slaughtered half his people [but] prior to the start of that scene escape ships were deployed for Asgardians — including Valkyrie.

^Source

There is also another instance of an Asgardian on Earth in the MCU through the ABC TV show Agents of Shield. Prof. Elliot Randolf, was confirmed to be Asgardian at 24:30 of Season 1 Episode 8 of Agents of Shield. (I just watched part of the episode to confirm). He lived permanently on Earth for an unknown amount of time. (Thousands of years).

This is just to provide another example of an Asgardian off of Asgard to support the theory that there may be more on other/unknown planets.

It looks likely that only a few of those rescued by Loki, Korg, and company (from the battle on the Rainbow Bridge) may have survived, probably escaping aboard Grandmaster Goldblum's pleasure craft (or escape pods we never saw) while the rest were killed. But it seems improbable they were the only ones.

First, Asgard ruled... er, maintained peace in a benevolent manner... over Nine Realms. It wouldn't make sense they did it from a single world, especially a large, flat-earth discworld asteroid with its atmosphere. They would have had to have a bunch of outposts and fleets of space-faring warships to supplement the Bifrost.

Mind you, Loki kind of let everything go to hell when he was pretending to be Odin, and when word spreads about what Hela did, and then Thanos (and what perfect timing that was, almost like he arranged it), those outposts and fleets are not going to be able to help Thor and the others because they will be very busy just trying to survive.

Second, it's also possible that not all of the survivors from the Asgard capital tried to escape using the Bifrost. Heimdall may have sent some to escape by other means. Space vessels may have been one way, but Hela would have locked them down after her return. The other way was revealed in Dark World when Heimdall said "There are other ways off Asgard, known only to a few", and we assumed only Loki knew of these. Heimdall and Odin probably did too, but they wouldn't be sharing that knowledge.

These other 'gateways' to other places could have been used by survivors, with the rest being either cut off by Hela's forces or deliberately trying to use the Bifrost to distract her while the rest used the other ways. This allows Thor's ship to get blown up in Infinity War in a manner that leaves no survivors but doesn't undermine New Asgard on Earth where any other survivors from fallen outposts can rally too.