A list of how many weeks a rotating game mode has been available for

Ascension 15 Legend of the Poro King 13 Nexus Siege 8 One for All 6 Doom Bots of Doom 4 Hunt of the Blood Moon 4 Dark Star: Singularity 4 Definitely Not Dominion 3 Hexakill: Twisted Treeline 3 All Random Ultra Rapid Fire 3 Ultra Rapid Fire 2 Hexakill 2 All Random Summoner's Rift 2 Nemesis Draft 1

Source from the League of legends wiki. (http://leagueoflegends.wikia.com/wiki/Rotating_Game_Mode)