Blocking only Flash and animated GIF images

FlashBlock will replace any Flash content on any website with a placeholder and play button (Firefox Addon).

SafariStand for Mac OS X will block Flash content in Safari similar to FlashBlock for Firefox.

NirSoft's TurnFlash allows you to easily disable and enable the Flash component in Internet Explorer.

TurnFlash is freeware and "standalone", and it doesn't require installation.

How to Stop GIF Image Animations from Playing in IE or Firefox

This also explains how to permanently block GIF animations in your browser:

In Firefox - Type about:config and change the value of string image.animation_mode from normal to none.

In Internet Explorer - Tools -> Options -> Advanced. Uncheck the box in Multimedia group that says "Play animations in web pages"

Alternatively to blocking animated images you can simply disable animation. Open about:config in Firefox and set image.animation_mode to once or none

AdBlock plus can block all Flash animation, but as far as I know it can't distinguish between animated and static gifs.

The filter to block Flash would be http://ad.uk.doubleclick.net/*.swf (for example). You'll need to train AdBlock for all the different ad sites.