I finally got an invite to Dribbble! (follow me here)
For the uninitiated, Dribbble is (in their words) a 'show and tell for designers'. It's basically an online community for design pros who want to share their work and maybe ask for feedback, or basically show off. It's pretty powerful, and can actually lead to paid work.
There are lots of posts about branding and logo design on Dribbble, and the ones that do really well (make the front page) are usually the ones that show a little gif animation. Sometimes it can really sell the story of a brand.
From my experience making banner ads and some video editing, I can do a pretty decent job of animating, starting in After Effects and then moving to Photoshop to make a lightweight gif. Here's a selection of posts I've made from some of my logo designs over the years.