Disclaimer: I built this service myself, but you can try http://grabicon.com. It's a very simple API for favicons that handles resizing and reformatting on the fly. It uses a lot of proactive caching for speed, as well. Like most other services like this, you can insert this directly into your HTML and it works great. I don't have online documentation just yet, but here are some examples using everybody's favorite web destination:
Get the icon in PNG format:
http://grabicon.com/icon?domain=microsoft.com
Resize to 64 pixels square:
http://grabicon.com/icon?domain=microsoft.com&size=64
This hunts down the icon using the various methods people can implement them, and uses the highest resolution version available, since favicon.ico files actually contain a collection of icons. It uses that version to resize to your preference, unless a perfect match is already available.
Let me know what you guys think, and what other features you might like!
UPDATE:
Grabicon is now back in operation, and it's not going anywhere. It was originally built for a customer who later decided not to support it. But now it's under my direct care, with much better speed and resizing capability.