The maximum amount of tenacity you can get from the new runes, items and summoners is 94.54%

http://na.leagueoflegends.com/en/featured/preseason-update/8000-8003?build=00112207

Full legend stacks: 20% tenacity

Both summoner spells on cooldown and recently used a summoner spell: 35% tenacity (for 10 seconds, then 20% tenacity until summoner spells comes back off cooldown)

Elixer of iron: 25% tenacity

Mercury treads and the active on new steraks gauge: 60% tenacity (the active lasts 8 seconds, and the tenacity stacks additively with mercury treads)

Cleanse: 65% tenacity for 3 seconds after using it

1 - (1 - 0.2) * (1 - 0.35) * (1 - 0.25) * (1 - 0.6) * (1 - 0.65) = 94.54% tenacity