I know Tom Baker and David Tennant are probably the most popular, but both my dad and I like John Pertwee best. I haven't seen all the Doctors, but out of the ones I have, Pertwee and Hartnell I found the most interesting. Hartnell, because as the first, he set the standard, and his travels took him to ancient cultures, and Pertwee partly because he was limited to Earth adventures. He didn't have the space trips to make his stories flashy; he had to rely on his own ability to entertain. I also loved his companion, Jo, more than any other. I think the fact that Hartnell and Pertwee were older than the other Doctors, makes them more interesting and quirky. They don't rely on dashing good looks to get fan girls interested.
The problem with the later Doctors is that while the stories and alien bad guys were appropriate back in the earlier days, now they just seem dated.