Is an animated favicon.ico a bad idea? Are there cool uses of animated favicon.ico out there?

Don't do it. The days of moving content without user consent are over. In fact don't use splash pages or auto playing video.

Users need to produce action for effects.

However, mileage may vary. There is such a thing a novelty design, this is the reason splash pages worked in the past. Just be sure what you do adds to the user experience not just yours.

Are there any creative or interesting usages of an animated favicon out there?

There's a playable version of the Defender game that takes place entirely inside the favicon.

There are two problems I have seen with this.The first is that it makes your website look like it is never done loading, because users normally only see the loading favicon animated and naturally associate any animation with the browser loading. The second problem is that animated favicons distract the user, just imagine having 8 tabs open and each one showing tiny animations.

Generally animated favicons will drive your page's UX down, but simple and descriptive static ones are always useful.