What are all of the games that have ever reached the #1 rank on boardgamegeek.com's Geek Rating list? The current #1 is Pandemic Legacy, and prior to that it was Twilight Struggle.
Strangely, Wikipedia had this information:
- Paths of Glory (August 19, 2001 - February 20,2002)
- Tigris and Euphrates (February 20, 2002 - 2002)
- Puerto Rico (2002 - August 2008)
- Agricola (August 2008 - December 2010)
- Twilight Struggle (January 2011 - December 2015)
- Pandemic Legacy: Season 1 (January 2016 - Present).
As Jefromi's answer shows, the dates aren't quite as nicely laid out as Wikipedia shows, but these are the games that have been #1 at some point in time based on persistent user ratings.
If we expanded it to games that rose to #1 because of bugs or user coordination, three more games are added: (1) The Game of Life, (2) Monkey Auto Races, and (3) Die Macher. The specific reasons for each are described on the Wikipedia page.
The games that have hit #1 are also listed on BGG in one of the Completely Useless Statistics threads.
As of December 29th, 2017, Gloomhaven is the #1 rated board game.
If you scrape all the versions of the current browse page on archive.org (that's sorted by geek rating, right?), you get this:
2009-02-05 Agricola (2007) 2010-04-07 Puerto Rico (2002) 2010-11-05 Agricola (2007) 2010-11-21 Puerto Rico (2002) 2011-01-06 Twilight Struggle (2005) 2011-01-16 Puerto Rico (2002) 2011-02-03 Twilight Struggle (2005) 2016-01-01 Pandemic Legacy: Season 1 (2015)
Note that those are the date archive.org scraped the page, not necessarily the exact dates the rankings changed.
The page was at different urls and formats before that (and wasn't always crawlable, it looks like) and I haven't bothered scraping any of them yet.