I just noticed that according to the main SE site, there's 110 SE sites. Which one was the 100th site?
First of all, let's see how many closed sites we can add to the list. There are 6 well known closes that happened some time ago. Smugmug was also closed, started Feb 8, 2012. Artificial Intelligence was probably the first closure. Also closed early on is Gadgets. There was a few other briefly lived ones as well, but I'm going to try to not count ones that never left private beta. All in all, I count 10 known (To me, with searching) site closures. That means the real 100th site was up a bit, that'd put it at Genealogy & Family History.
taking all currently listed sites, sorted from oldest (http://stackexchange.com/sites#oldest), taking the 100th element (
$(".lv-item")), yields the answer:
100th .. 103rd oldest currently existing sites (excluding private betas and area51) are these sites with the same age:
http://area51.stackexchange.com/?tab=beta (thanks @PearsonArtPhoto for the link) gives their age in greater precision and disambiguates this site as the oldest of these four, and thus the 100th oldest currently existing site: