Today I stumbled across a new website called MoonBase, which lets you very easily create simple animations (such as in this example) and embed them into websites. I can see this as being a very useful tool for adding basic animations into questions on StackOverflow, in order to discuss an animation that may otherwise be difficult to explain. This would provide a really nice visual improvement of a question without the need to come up with something new.
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I think this is a very bad idea, and I'm opposed to it.
Many proxies also won't allow this sort of site to be accessed. If there's a large portion of the answer dependent on the embedded animation and it's not available, the answer becomes less useful. (There are already issues with the image server being used on SO being blocked by corporate proxies such as the one where I work. Animations instead of comprehensive text would make many questions and answers unreadable or inaccessible.)
The same issues with proxies can also happen if the off-site server is down or unavailable for some reason. The answer becomes considerably less useful.
Also, some countries and regions still have low-bandwidth connections. A link instead of an embedded animation allows them the choice of viewing it or not.
I think that answers should remain word-based, with images used (sparingly) to clarify, and any additional off-site information should be included as a link with explanatory text.
See also this previous Meta question about allowing embedding videos in questions and answers.