The highest floor I've ever lived on for more than a week is the 9th, and I recall seeing pigeons roosting outside my windows.
I'm guessing that there is no point in going beyond maybe a hundred feet or so. Their predators may chase them higher or they may chase prey higher, or maybe winds are favorable for long migrations at certain altitudes, but other than that why fly high?
Of course at some point the oxygen levels would be too low, and for something as metabolically supercharged as a bird I'd guess problems would start sooner than for other critters.
Silly me, thinking when I could have checked out the Straight Dope. There's more here, but it's suspect because Paul Ehrlich's name is on it (google "Paul Ehrlich error" and you get well over 100,000 hits).