My crashes happen when I have the LoL launcher running in the background. It's not even a crash - The game literally closes within 0.3 seconds smoothly, no error mesage, no Windows error sound, nothing written into logs, no harddisk access, RAM immediately available. The crash is so smooth it's actually better and more swift than shutting down the game via the menu.
 I figured out later the LoL client has changed to be running on the GPU and since I close it and/or reboot, all is fine. Could imagine some other GPU-related task might cause problems (e.g. hardware-accelerated Flash/HTML5 players like Youtube's) or software aging that causes them.


On a freshly rebooted system, I never had any of these random crashes.