Just logging for the record that I am having this problem too. A few observations:
1) it's affecting many but not all of my https:// sites. All google (gmail, accounts, google.com), LinkedIn, Yahoo, Facebook, Wikipedia even are not displaying - generally all because 'Safari cannot establish a secure connection to the server'. Oddly though, sites like https://www.twitter.com are working.
2) I loaded Chrome up as well and the same sites are affected/not affected. I get the message No data received (ERR_EMPTY_RESPONSE) in Chrome.
3) Prior to mucking around with some Network settings this morning, if I hit Command+R approx 10 times the secure pages would load correctly. After removing the only extension installed, clearing caches and cookies, disabling DNS pre-fetching, etc, none of them now load at all.
I'm running Safari 9.0.1 on El Capitan, which came preinstalled on a brand new MBP 6 months ago (and was working fine until 1-2 months ago). All of these sites display correctly through a high end HP Win 10 laptop running in parallel here so it is not the router/network config. Given multiple browsers on the same machine are having problems, it looks like something in the networking within OS X is the issue.
D'oh. Will call Apple Support shortly...