Or the remote lib could return sprite coordinates and dimensions, and serve one composite graphic.

Gravatar is used all over the place and is almost always hotlinked. Download if you want and you know the set of types you need icons for. Otherwise, it's just easier to blindly hotlink.

Gravatar has avators for all its users, which could potentially include everyone online. File types icons are much more limited.

The rank of the first set is in the multi-hundred millions, while the later can be ~50. There is enough room in my /var/www/pub/images for 50 x ~40kB. (my entire disk storage, 300GB, can only hold avatars for 63M people.)

If the user has visited someone else's site, they may have the hotlinked image cached and thus your page will load faster for them.

As pierrfar has shown, they disable any caching, so even if you use the same icon on several pages of your site the browser will have to re-download it every single time. Now all they need is to to log the client IP and client agent string and they have a fairly accurate global clickstreams for all users over all sites that use this service (not to mention what they could do with a cookie).