Update: A couple hours later, League of Legends NA is back up. You may hit a short queue upon logging in, but that's about it.
Currently, League of Legends is indeed not working like it should. At time of writing, the game is failing to display Summoner info, the store, and other content. When attempting to log out via client, it simply locks up, requiring players to close League down directly from the taskbar.
Attempts to log back in are met with errors, at least after you've been informed that the servers are not responding. Don't worry: you are not alone.
Riot Games has just updated the official LoL Status Twitter, confirming the issues for North Americans.
We're currently investigating issues with NA. Sorry about the inconvenience.— LoL Status (@lolstatus) November 19, 2013