PJ68 is right, original movie from 1979 or so with Carol Kane as the babysitter. The first 20 mins are often remembered as some of the most terrifying and suspenseful in cinema. Keep in mind, back then there were no mobile phones, or the technology we have today, and babysitting was still a pretty common and mostly worry free position for young girls.
I dont know why they did a remake, although I am not one of these anti remake people, it still just doesn't lend itself to a remake of that type of film. Doesn't every young girl have a cell phone and pager these days or some way to communicate? Anyway, not sure it did well here..