Double G Studios, the London-based animation and video supremos, developed the moving image logo to reflect the Tate's continued support of film and tv arts coverage on its own Tate Channel. A video of the result isn't currently available, but there are a few stills of it -

To some extent TV has pioneered this already, with BBC, Channel 4 and Sky in particular flirting with dynamic branding, where the corporate identities ardynamic and only ever partially in complete view. So its only a matter of time before the bigger brands and organisations unrelated to broadcasting decide to go down this route. It just takes a few early adopters to start the ball rolling.
The trouble is that this sort of re-branding won't come cheap. You can't just fiddle with an established corporate identity and just animate it. Dynamic branding will mean devising and creating a whole new visual concept across all forms of media. Clients will be taking a risk, so they will be looking for cohesion and clarity as well as stunning ideas. A recent example is the re-branding of Swisscom, and here is a great video clip of the design process that produced one of the first truly dynamic brand identities -
There is plenty more to look at and read about this ground-breaking project at Moving Brands Agency website.
Does this mean the end of the static logo? Probably not, but it does mean a great deal of new opportunities for graphic and digital designers, and whatever happens, eventually we can count on the new retro look - the simple, static, black and white logo - and we'll almost be back where we started.