When a male American Robin is establishing his territory, if he's at the edge of his territory and another male robin approaches, he may lower himself in a display called the crouch. Any other male robin knows that this is a warning, and that it may signal the bird's readiness to attack.
While perching, European Starlings often spread their wings and move them in a strange rotating fashion while issuing their squeal-call. They do this most commonly just before pairing in the spring, and on warm fall days. In the spring this display, known as the wing-wave, seems to be a long- distance advertisement of the male for a mate.
If you're interested in learning more about displays and bird behavior in general, you should look for a wonderful book, often available in libraries and bookstores, which describes displays for twenty-five of North America's most common birds. It's A Guide to the Behavior of Common Birds by Donald Stokes, and published by Little, Brown and Company in 1979. It's worth looking for.
Also, don't forget about our short story about one year in the life of a House Sparrow, in which many of that bird's behaviors are described.