I have this same issue. It was recently too, as of the new patch they put out today. Champion select is fine, but on the loading screen LoL.exe crashes several times and I have to keep logging out and back in up to eight times just to get into the game. It'll load champions to a certain extent than just goes down. So far I'm not the only person having it, a few members of the opposite team have been experiencing too.
Someone asked if it was my connection, but it's not. Only the LoL client is crashing, nothing else. Any idea when this'll be fixed? It's a pain in the butt to keep relogging just to get into the match.
Also, apparently it's bugging the friends list as well, still registering me in-game when I'm not.