Just cruising around looking for links here... this is a pretty cool story about crows. I did know about the twig stuff, but this was in a study, where a crow unexpectedly grabbed a wire, flew off with it, and used it to make a hook and get the food they had put in a bottle:
http://news.bbc.co.uk/1/hi/sci/tech/2178920.stmThe tool story I remember most was of a crow using passing cars as a tool to open nuts. It would sit on the side of a highway, watch the cars go by, then get a nut, put it in the path of the tire tracks, and wait. A few cars would come by, eventually crushing the nut. Crow hops down and eats it, then goes to find another nut and repeats the process. They're definitely very, very smart.
Right at the moment I can't find any online resources for parrot tool use, but more than other birds, even, parrots are very tactile with their feet and use them almost like hands. Alex, the famous CAG (Congo African Grey), learned to request objects, and one of the objects he requested frequently, rather than being food, was a metal key, so that he could use it to scratch under his beak. Their tool use is broad, and I'll have to look further to find more instances of it... at the moment I'm about to go to bed. =)
One anecdote from Bird Talk that I remember, though, shows contextual intelligence and problem solving (and is just really funny). The Grey in question had been told many times when being offered an object "Use your claw" -- assumedly the bird would grab first with its beak, and the owners wanted to teach it to accept things with its claw instead. The family had a football party and were watching the game on the big screen -- eating, talking, not paying attention to the bird. The guy on the screen fumbles the ball, and the bird pipes up: "Use your claw!"
In another instance, a family was selling their couch, and the buyers came over to pick it up. Their Grey flew over, landed on the couch, and announced "I pooped here!" Sure enough, he had, and the sellers hadn't noticed. Oops. The bird had not been known to do that kind of thing on other occasions. The somewhat scary thing about these birds is that they can hear something once in context and apply it months or even years later, unexpectedly.
Their behavior is incredibly fascinating. In some ways it's very intimidating to be pursuing the prospect of owning one. (And a bird like that more owns you than you it...) But I would very highly recommend Irene Pepperberg's book. Very little of it is the clever anecdotes, but there's an extremely thorough documentation of her research process, and of Alex's behavior throughout. He surprised them a number of times, and it's nothing short of staggering what they're teaching him to do. They're hoping that eventually they will teach him to read. Pepperberg's work has been used, in addition to the animal behavior field and the whole of our perception of animal cognition, to help children with communication disabilities, since she's tracked down much of the way that Alex learns and some of it has a direct analog to developmental speech in humans.
The next book I'm going to track down in the animal behavior category is, I think, _Next of Kin_, by Roger Fouts. It might be another one, I have the exact book info written down on my laptop... in any case one of the more highly praised books about chimpanzee intelligence.