EDIT: yeah, so my little hosting package didn't agree with your interest (you consumed 12 times my allotment). Fortunately the nice people at OSM.be came to the rescue and offered me some space. Thank you Ben!
I have a big scheme in my head to do somehing fun with OSM data. Unfortunately I'm still taking babysteps. Still, here is one step that makes me pretty happy: a map of the evolution of La Paz, Bolivia. EDIT: as I'm a disaster in reading manuals, I didn't add timestamps to the first few tries. I'll re-run them with timestamps when I get the time.
I can make an animation like that for any bounding box with just a couple of minutes work (and some waiting time, depending on the data-density of the area).
In fact, doing this is extremely easy. It still took me two months :) All you have to do is follow the instructions here: https://github.com/MaZderMind/osm-history-renderer/blob/master/TUTORIAL.md (this was very helpful too: https://github.com/MaZderMind/osm-history-splitter)
Only for me, that meant setting up a VirtualBox with Ubuntu, understanding how to install software on Ubuntu and how to fix messed up installations, getting Ubuntu to be able to read data from my host Windows 8 laptop. A big challenge was also not throwing the laptop out of the window (everyone LOVES Windows 8, right?). I could have not done this without Mazdermind Peter who didn't just make the data available in a workable format and the tools to work them, but also gave me personal support. Eternal gratitude and what not. Also free Belgian beer (or chocolate) on any future IRL meetings.
If you want something similar for a bounding box that interests you, let me know. Just send me a bounding box made with http://maps.personalwerk.de/tools/bbox-paint.html and send me the "EPSG:4326" line. That way I can stupidly copy paste the coordinates.
Next step: creating yearly statistics about the state of the map.
Here are some requests:
EDIT: Peter suggested I make an extract of my setup for him to distribute. That would mean you can install VirtualBox (easy), load up a copy of my VM (should be easy), write three lines of codes and you have your thing (easy).
EDIT: There are some bugs visible (Krakow, Kathmandu). It might be I failed to do an update for some of the involved packages. If after a re-run they still show, I'll try and make some bugreports for Peter.