When I first began using Google AdSense on this website, roughly a year ago, I had Text ads only and Text & image ads selected as my ad types (mainly to experiment with the different types). I quickly saw that the Text & image ads displayed Flash based ads. I do not like Flash, and it would be hypocritical of me to run Flash based ads, so I switched everything to Text ads only.
However, sometime within the past couple of months, I noticed the Ad type dropdown menu in Google AdSense no longer listed Text & image ads but now listed Text & display ads. Ever since selecting this new option, I see animated ads that are no longer Flash based.
This is a welcome change that I think most of the Internet will appreciate (seriously, Google search it, people hate Flash based ads).
Update 2013-08-23: Well, it looks like I am wrong. As mentioned above, I do not like Flash, and I refuse to install it, so I only use it through Google Chrome. I primarily use Safari and Firefox, and I did not consider that Google AdSense would check to see if Flash is installed and only display Flash based ads if it was. I kept expecting to see the Missing Plug-in error in Safari and Firefox.
Update 2014-01-16: Turns out, if you log in to your Google AdSense account, click Allow & block ads, and click the Ad serving tab, there is a toggle at the bottom under Display ads to allow or block Animated display ads. Flash and GIF based ads will no longer be served if this toggle is set to block. If only Google would turn this toggle into two toggles: one to allow or block Flash based ads and a second to allow or block GIF based ads.
Update 2015-02-27: Looks like Google is converting Flash ads to HTML5 ads if you don’t have Flash installed.