Does the same for me, the full error text is : "The launcher has experienced an error. Please restart this application."
Now, I know what the answer will be. Re-install the game, that will fix it. However, the last two patches have prompted the same error message. Both time I reinstalled, fixing the problem. I REALLY don't want nor should be expected to reinstall the game every single time a patch comes out, which, in the case of LoL, is basically every week. I hope this issue can be resolved soon.