Every application icon that is exposed to the operating system must exist in at least nine sizes.
16, 32, 48, 256 are more or less expected. These are used in "small", "icon", "tile" and "extra-large " views in Windows Explorer.

20, 22 and 26 are possible sizes of an icon used in the window caption. The exact size depends on screen's DPI level.

And 40 (along with 32 and 48) is the size of an icon used in Alt-Tab view on W7, again depending on the screen's DPI.

If you don't provide an appropriately sized icon, the OS will grab one that is slightly bigger and shrink it down, ruining the pixel polish.

Lastly, each icon ideally must be saved in 32, 8 and 4 bits per pixel formats, so to be compatible... you know... with EGA cards

It would've not that big of a deal if it weren't for the size of a resulting .ico file. For example, the above icon ends up being ~ 120KB, whereas the actual .exe it is attached to and that does quite a few meaningful things sits at around 96KB.