Crows exhibit some remarkable brain power. In particular they can problem solve on the fly (so to speak) as seen in this video: http://news.bbc.co.uk/2/hi/science/nature/8029933.stm
I read an article (sorry I cannot find it now) where some crows spotted a rabbit but, being unable to kill the rabbit on their own, antagonized a hawk they knew to be in the area. The hawk gave chase and the crow flew towards the rabbit. When the hawk saw the rabbit it decided dinner was offering itself and swooped down to kill the rabbit. The crows did more though, another crow was apparently on the ground near the rabbit making itself known to distract the rabbit (so the rabbit would not see the hawk coming). Once the hawk killed the rabbit the crows mobbed the hawk and ran it off leaving the crows with a rabbit dinner.
Crows in Japan like a particular nut but the nut is too tough to crack. So the crows stand on street lights and drop the nuts into traffic below which the cars break. Then the crows swoop down and get the good parts (as can be seen here).
In another case researchers wore masks while raiding nearby crows nests for research. This did not please the crows at all. Thing is they remembered those faces and would react for years afterwards when they saw those faces. More, other crows learned who the “bad” people were and joined in.
In my own experience I spotted an injured crow on the ground and went to see what I could do. Its friends were in the tree above and started cawing to distract me. When that didn’t work they started breaking off twigs from the tree and dropped them on my head.