Yeah, I'm going with, I assume SHIELD took it.
It clearly took the Bifrost to get it to Earth. That says to me that Odin couldn't retrieve it without the Bifrost. I assume that Loki could... but Loki is... busy. I do think it's worth wondering whether, once Loki gets his act together, it occurs to him.
I'm also kind of assuming that its not meant to be destroyed, in keeping with how tough it is in the comics. Didn't we see it falling more or less intact? I don't think the fall would have damaged it, either. Thor managed to shut it down, but I didn't assume he managed to render it forever unusable. The sequence with Sif made it seem like it can self-repair.
The way they seemed to play it, Loki was able to see/hear through it and control it from a distance... but I was left wondering if that was particular to Loki and his magic, or if it is supposed that way for Odin as well.
I think most of the GA probably assumes it's destroyed, but at best I think Thor was just knocking it out for a long enough period for him to go and take care of Loki, which would in turn stop the immediate threat of the Destroyer, without Loki continuing to control it.
So my question is: if it's in SHIELD's hands (and why would Coulson leave it lying there, even if he thought it would never work again?), has it self-repaired and is just dormant? Could Odin make it do anything remotely, even without the Bifrost? Will Loki think to come get it? (Could he do anything to it, now that he isn't in Odin's position as king and no longer holds Gungnir?) ... Will we ever see it again?
(Part of me hopes so, and part of me agrees that since it's been a big set piece for the first film, we're kind of unlikely to see it featured prominently again. Especially since the audience saw Thor deal with it relatively easy once already. Which, as many people have already said, is a pity.)