My understanding of how this project started is hearsay so don't take it as true for granted (in fact if you know better, send me feedback).
In about 2004 Vladimir Vukicevic and Stuart Parmenter (both of the
Mozilla foundation) started working on an animated version of the PNG
format. PNGs are superior to GIFs in several important ways but
unfortunately support no animation.
MNG already existed at that time but was too big/fancy for most people to accept as an image format (this is the first and last time I mentioned this flamy topic).
Out of discussions on the PNG mailing list, bugzilla.mozilla.org and lots of other feedback a preliminary spec for APNG was born and revised four times.
Then Vlad and Stuart had no time available for APNG so it was left as a todo for a later time (2 years it turns out).
In the spring of 2006 David Humphrey
of Seneca College arranged for
me
(Andrew Smith) to meet with Vlad and work on APNG as a Google Summer of Code project,
to inplement the APNG spec into libpng. This was completed successfully
for libpng-1.2.10.
In the fall of 2006 I updated the patch to work with libpng-1.2.12
and integrated it into the Mozilla tree. The patch is awaiting aproval
(see bug 257197).
In Winter 2007 I turned the spec and the patch inside out more then
once to accomodate everybody. Still awaiting approval.
20 March 2007: the patch got into the mozilla trunk, happy day!
21 May 2008: After maintaining the patch for a year I've decided to move on to other things. Hopefully someone else will continue to update it for new versions of libpng.
25 September 2010: I should have mentioned this here a long time ago. As you can see from the list of patches below Max Stepin has been very kindly maintaining the patch for pretty much the last two years. Say thanks to him if you're using APNG outside of Firefox!
5 Feb 2011: Also, the Animated PNG website has been maintained by Max for a while. That website (originally created by Brendan Sera-Shirar and his students at Seneca) is a much nicer version of this one :)