The best one to start off with is "Rose", like the people above me said(even though I started with "The Impossible Astronaut").
If you really want to go back and start at the very beginning, "The Unearthly Child" is the first episode. I think it's still on YouTube, and if not, it's on DVD somewhere in te vast expanse of space and time.
But for the modern Doctors, start with "Rose". :)
I would strongly advise you to start watching from the beginning if you want to know the whole story. Start from the new Doctor Who series. The best episode to watch first is "Rose", the start of the 9th Doctor
If you were to dive strait into doctor who either series 6 or the new on that's coming out fall 2012, than you will most likely be very confused and put off the series. so you should start with the the new doctor who ie. from 2005 with Christopher Eccleston "Rose". you wont be lost and you'll get a lot more of the humor.
I would start watching from the beginning of the new Doctor Who era like everyone else says. Then if you like those episodes and want to watch other episodes from the classics you could watch a few on Netflix or on Youtube.