I have seen others talk about a Zendesk Talk Mobile App, and I see that Caroline has suggested that a standalone Talk app may be in our future.
The feature that would be the most useful for us in terms of a Talk Mobile app would be a way to toggle Availability status from Online via Browser to Online via Phone to Offline.
I manage a (very) small team with other tasks and a low-but-variable call volume, so we frequently forget to swap to our phones or to go offline when we leave our desks. More than once I've been served a call when out at dinner! It would be nice if we had a way to change our status without having to get to a browser or contact our (only) admin to get to a browser for us.