We're aware of an issue going on at the moment causing some players to be unable to log in. We're working closely with other teams at Riot to figure out what is going on and resolve. I will provide any updates here.
Thanks for your patience while we work on this.
UPDATE: Thanks for all of your help with the logs everyone, very useful! No need to send any more through.
For a good breakdown of the issue please see Riot Zaps' post below.
**Update 3:38 PM AEST:**
A change has been made that looks like it should resolve the issue for most players! Please let us know if you're still seeing the issue after the time this post was updated!
Some players in other regions may still be unable to log in. Other teams at Riot are currently looking into fixing this for those regions. THIS HAS NOW BEEN RESOLVED.