This thread is an attempt to condense the information of the many previous avatar threads.
1. Avatars have a maximum size of 100px by 100px.
2. After changing your avatar, press Ctrl+F5 (may differ by browser - look for the 'clear cache' option) to refresh images on the page
3. Due to an unknown issue with SMF (God if there aren't many of those) linking to avatars on https sites may fail. It is usually safest to download the image, then reupload to BG.
4. If you absolutely cannot get it working, you may want to try
http://en.gravatar.com/ - or of course make a post in this board.
I'll leave it unlocked for people to post other tips about avatars.