Does only GIF support animation?

Solution 1:

Taken from the Meta Topic on Post Formatting, an animated SVG file:

^{Image author: Pumbaa80 via Wikimedia}

NOTE: This is not widely as accepted as GIF, so things like some versions of Internet Explorer will show the image by default but it will not be animated.

Solution 2:

There is a format of PNG out, APNG, that does what GIF does but better. It is still not supported in all browsers, but it is on the rise.

Edit:

Since the libpng(used by blink in chrome/opera/chromium) committee has locked up, and as it does not seem like any changes will come soon, a better choice might be to use Video with alpha-channel.

Shown here: Video transparency Example