I am going to talk technical stuff here for a bit. I hope you'll forgive me.
I love animated images. I composed a few animated images back in the earlier days of the internet. Not many, mostly because I found it a bit too time consuming, but I did assemble several. When I learned of the differences of PNG over GIF, I essentially swore off using GIF for anything -- except animations. PNG is, by far, a superior image format due to the capability of using indexed or RGB colors, and having full support for transparency on each pixel. With PNG, you can have smooth transparency around the edges of an anti-aliased image, while GIF requires you to spend one of your 256 colors as an alpha mask. This means every edge is pixel sharp -- sometimes desirable, but not always ideal.
Then, a while back, I learned of the APNG specification -- an unofficial extension to the PNG format which had, it seemed, been declined simply because it competed with the PNG Group's MNG specification. I decided to test the waters with this and hunted down the tools I would need to build an APNG. My first animation or two were tiny conversion of animated GIFs, just to see the format in action. Satisfied with its performance, I proceeded to take a fan-made Sally Acorn spritesheet and compose this image
from it. And it is a shame that APNG was turned down, too. I recently got a comment that PNG images aren't animated -- which is technically true. In Firefox and Iceweasel it should display automatically, but every other browser requires a plugin (and not all browsers have on available) to display animated PNG images.
So there are four relatively easy ways today to make an animated image -- and please note that I only mean animated. These formats do not require support for sound. The first is the old standby, Animated GIF. Thanks to its age, and the expiration of patents on GIF, it's all over the place, now more than ever. Unfortunately, it's used in a LOT of circumstances where it is an inferior file format due to its limitation to 256 indexed colors. In particular, I mean animated video clips. Take stills from a video and stitch them together as a GIF and... well, I wouldn't put a GIF up on a website to illustrate a movie, let alone to portray part of it, whether said movie was live action or animated (though some animation styles are fair to be represented in GIF, not all are). GIF is so widespread that it is a standard in all modern internet browsers -- no plugin required.
Second is MNG -- this has limited browser support, since Mozilla dropped support for it in 2003. This is the PNG Group's alternative to animated GIF, and has a more cumbersome implementation than PNG, but does offer a large number of features. If you wanted to make an animated movie, MNG would be your best bet next to our next format -- and possibly the best choice of all if you plan to use raster, or bitmap, graphics. However, unless you use Konqueror, MNG will not display in your browser without a plugin. It is supported in a number of free or open-source, or free and open-source, image editors,
Third up is perennial animation tool: Adobe (née Macromedia) Flash. This is actually a highly impressive choice that has come quite a long way over the years. The catch? Like MNG, you generally need a plugin. However, the plugin is easily available due to the persistent prevalence of this presentational prodigy. Some sites are built entirely on Flash, so you generally can't experience the whole of the Internet without the Flash plugin in some form or another. If you want sharp, crisp animation or any sort of interaction with your animations, SWF is the way to go. Also if you want to make a TV show, Flash is becoming a powerful component in the 2D animator's arsenal of awesomeness -- Shows such as My Little Pony: Friendship is Magic are made almost entirely in Flash (MLP, specifically, is made in Flash 8, i.e. the version before Flash CS). Of course, Flash was being used professionally before that: series as diverse as Clone High, Metalocalypse, and Danny Phantom have all been made using Flash. However, Flash has one drawback: It's not just for images.
Finally, there's Animated PNG. This fairly lightweight extension to the PNG standard will gracefully fall back to a still image in any viewer without APNG support, allows per-frame timing, and unfortunately requires a plugin unless you use Firefox or Iceweasel. This requirement of a plugin is a serious problem -- but one that will remain unless the PNG Group can be convinced that APNG either occupies a unique niche in lightweight animated imagery, or that MNG is not a viable platform for animated imagery.
There are other ways to get animations up online, like Animated SVG (I'll pass until there's a toolkit as easy to use for making an Animated SVG as Flash is), or CSS Spritesheets, or even JS hacking to load and switch images either through a spritesheet or image sequence method... These are cumbersome replacements still in the early stages of development, or altogether lacking for a simple, lightweight animated image solution. So I'll keep throwing my support with Animated PNG and Flash for my animation work -- or using a full-fledged video format buil through Premiere.
So please note, any animations I post from today onward will either be SWF or Animated PNG -- I strongly believe that we need a lightweight animated image format (MNG is not lightweight) that supports proper transparency (Animated GIF supports only index transparency, which is 1 bit of transparency data). And you can expect to see a few animations from me over the coming year, both in pixel art (APNG) and Flash animations. Any animations not in one of these formats will be featured on my YouTube page, as those will be in the form of a pure video file, most likely an h.264 MP4 video.