What is an ideal size for a .ico file, that would sit in the top corner of a window?
Answer
Short answer: 16 x 16 pixels.
Long answer:
.ico files can actually contain multiple images, at multiple colour depths - you can provide 16x16, 32x32, 48x48 and 64x64 in a single file and the OS will pick the best one to show.
Of course to keep the file size low you don't want to put too many in there, but if you think people might be saving a link on their desktop (say it's a web application) then it's probably a good move.