The ol' Grandfather Clause

I read your column in the archives on whether time travel was possible, and you mentioned the Grandfather Clause, where if you go back in time and kill your Grandfather, it would become impossible for you to have been born, and so you couldn't have killed your grandfather, which is a big fat paradox. So what's the deal? If you went back in time and killed Grandpa, would the universe just alter itself to fit your actions, or would you get booted to a parallel universe where the consequences of your dirty deed play out, or would something even freakier happen?