There's a new paper out by the group of Nicky Clayton, Cambridge, in the April 4 issue of Current Biology. I know Nicky from the Social Science Research Council sponsored workshop "Behavioral Organization in Animals" in Bodega Bay (see program).
In their study, the researchers used the popular ‘trap-tube’ task to assay the extent of physical cognition (specifically, an understanding of the operation of gravity) in rooks. In the experiment, food is placed inside a horizontal tube which has a vertical, blind-ended tube attached to it. The animals had to push (or pull) the item from the appropriate end of the tube using a stick, so that they do not lose the item in the trap. Seven out of eight rooks learned the task and all seven passed a transfer test, in which the food had to be dropped into the trap to be accessible (see picture).



The authors hypothesize that the rooks have a sense of gravity ("physical cognition") and may use learning to abstract rules to acquire it.
There was a fairly recent (2002) report in the journal Science by Weir, Chappell and Kacelnik, who showed that New Caledonian crows are able to shape unfamiliar materials to create a usable tool for a specific task.
These corvids don't have birdbrains, it seems