An .ico file is a visual representation of something else, usually another file. Web pages can be linked to icons, which will then represent the page in visual contexts. This page is represented by this icon: Where the icon is present, the file will be easier to see and easier to recognize. See Microsoft's favicon page.
Pages defined as Favorites in Internet Explorer will show their icons like this:
Hoppa.com displays favicons from the pages listed. My educated guess is that google.com and the others will soon follow.
The favicon is shown in the navigation toolbar of the Mozilla browser:
This is what Opera looks like; first 3 "anonymous" pages, then 3 with favicons:
In modern directories, like hoppa.com, the favicons are shown, increasing the visibility of their sites

All browsers I test, seem to use the same image for all sizes of an icon. The smallest image in the icon file, or simply the first? IE does the better resizing job here, but displaying a 16x16 resized to 48x48 is a waste, when a 48x48 original is available.
| Åge Utnes | |||
| Atlantstøkni | |||
| The B-52's | |||
| Bikez [A single resolution (32x32) icon, causing IE to miscolor the background] | |||
| Smyril Line | |||
| Drekkedagsnatta | |||
| Body World | |||
| Dumdum Boys | |||
| Farodane | |||
| Filadelfia | |||
| Faroe Islands | |||
| Føroya Banki | |||
| Gríma | |||
| Byens lys | |||
| Måne | |||
| Norway | |||
| Stavkirke | |||
| Arthur's Round Table | |||
| Hearse | |||
| Mortal Love | |||
| NATO | |||
| Red Cross | |||
| Føroya Sparikassi | |||
| Heimagreiðslan | |||
| Jarðfrøðissavnið | |||
| Havnar Sjónleikarfelag | |||
| ICI | |||
| Sansir | |||
| Tryggingarfelagið Føroyar | |||
| Føroya Lív | |||
| Heckler und Koch | |||