Vocal learning has been repeatedly demonstrated in two bird orders, Passeriformes (specifically, the oscine songbirds) and Psittaciformes (parrots), and, most recently, the Trochiliformes (hummingbirds). These three groups are widely separated from one another on the avian family tree, but their brains are quite similar. The same areas that control song learning and song production in songbirds and parrots are also present in the brains of hummingbirds. It was found that the songs of green hermit hummingbirds living in Costa Rica are different from those of the same species living in Trinidad. Weird.
[Editor's note, 9/12/2007: momomom has pointed out that it is indeed possible to band hummingbirds; organizations such as Operation Ruby Throat (at http://www.rubythroat.org) do this on a regular basis.]