The first use is OK, the second isn't. The Microsoft spinning earth widget, for example, is a pretty low key deal compared to some antics you see on the web. Sports cars zooming across the screen, bomb blasts and the like are frantic distractions in most cases. If you've got a bunch of frantic activity going on in a place where you're doing your utmost to sell a product or service or perhaps impart some critical information, the effect isn't likely to be positive. Of course if you're in the business of selling software to make animated gifs or programs that run them, you'll want to put a bunch on your site.
Games are another example.
Inner Images can animate anything you think should move. The author is an Individual Member of The Association of Internet Professionals.