I signed up for FeedBurned way back when, but didn’t use it for quite a long time. Only recently have I started to review its functionality.
One very obvious benefit it provides is to provide remote access to locally based consumers. For example, I use planetplanet to aggregate some of the blogs I publish. If I ran this service on the same servers as the blogs, there would be DNS troubles because of the way I have my network setup (the names resolve externally, but not internally).
What I’m realizing is that I could just use the feedburner address, and then my feed publishing software can also act as feed subscribing software without having to do much DNS footwork.
Its not setup yet, but I like this idea!