Deals.Woot

I would start with Christopher Ecclestone, then Tennant and Matt Smith if you're still liking it. Once you're current, you can go back and watch some of the classics. Tom Baker is the best Doctor, and that's a true fact.

edit: Maybe skip Ecclestone.

It depends upon how you like cheap special effects and if you like BBC programs and if you like old sci-fi programs. If you like all of the above, start at the beginning with the first Doctor.

If you are younger and don't handle cheesy effects well, start with Christopher Eccleston's (the ninth Doctor) re-launch of the series which originally aired in 2005. This will give you the background for the David Tennant (tenth Doctor) transition (many people love David Tennant's version of the Doctor and swear that he is the best). Then catch Matt Smith (eleventh Doctor) who is the current Doctor (I am a major fan and believe he is fantastic).

DEC 25th - Doctor Who specials are better than Christmas presents

I loved Eccleston, but he played the Doctor at a different place in life. Tennant was FANTASTIC, and Smith isn't far below him.

I've watched a lot fewer of the real classic episodes. They're all products of their respective decades, but they also have many similar qualities to the 2005 reboot of the series, in terms of tone (although the more modern ones are more fast-paced).

I started in the last 5 months or so on Dr Who (so welcome to the club soon) - I felt way behind the power curve too. I started on the new series (Eccleston) and worked from there on netflix. Then started watching Torchwood. I plan on hitting the classics and other spinoffs later.

I agree with starting with 9th Dr. (2005 season) and then going back when you are caught up

Start with Eccleston, just make yourself hang in there, you won't be disappointed. The show is still a bit cheesy at that point, but the characters are great and just continue to get better. Make sure to sprinkle in some Tom Baker, there are lots of the fourth doctor's adventures on Netflix.

I'd start with the Eccleston series. He's a great Doctor. He's not as whimsical as Tennant nor is he as bat (profanity) alien as Matt Smith, but he's dark. He's got issues and he lets them come out. Plus, there's a whole bunch of back story that you'll miss if you don't watch his series, especially if you want to see how Rose became so attached to the Doctor.

Agreeing with basically everyone here, start at the beginning of the reboot with Christopher Eccleston. It's a bit campy, but you'll need the background for later stuff and it really does get better by the end of season one. If you like what you're seeing, and think you might like a more adult take on the universe, intersperse Torchwood where it was aired with respect to Doctor Who. This is how I'd do it:

Doctor Who series 1
Doctor Who series 2
Torchwood series 1
Doctor Who series 3
Torchwood series 2
Doctor Who series 4
The Next Doctor special
Planet of the Dead special
Torchwood series 3 (Children of Earth)
The Waters of Mars special
The End of Time special
Doctor Who series 5
Doctor Who series 6
Torchwood series 4 (Miracle Day) aired in the midseason break during Doctor Who series 6, but it was pretty bad... I wouldn't blame you for skipping that one.

The list may look a little intimidating but if you like the show, you'll find yourself powering through it!

I started watching episode one of what ever was on netflix. Made it through about 3 episodes and got bored. I had such high hopes since everyone I know and their mothers enjoy the show.

@kidincredible: Agreed on all points, especially Capt. Jack. Such an awesome character. Handsome too, if you're into that. Not that there's anything wrong with that.

@rprebel: Straight dude and I'll totally say that John Barrowman is ABSOULTELY easy on the eyes.

I have to say that I stumbled upon The Doctor while trying to find something to fill the gaping hole left by the end of Battlestar Galactica and the general disappointment and failure of Caprica. I started watching just when Matt Smith took over as the current Doctor and have been able to follow along fairly easily; i.e. jump right in and enjoy, fill in the gaps as you can.

I would tend to agree with most of the posters on here that for a general sense of history, go back to the first season of the current iteration of the show with Eccle...what's his name. David Tennent then takes up the reins and was a real favorite with the Brits while he was doing it; your average American will recognize him from "HP: Goblet of Fire" as the Marty Jr. character who disguises himself as Mad-Eye for most of the film. Matt Smith is now playing the Doctor and is going into his third season (ps - as I understand it, what we Americans refer to as a season is known as a series by the Brits.)

@wootfast: not true, especially for the casual viewer. There are certainly undercurrents and foreshadowing throughout the episodes, but many of the episodes are just that and can be enjoyed on their own.