OK, I'm probably showing my age here, but I can actually remember when police boxes existed outside of a television studio. There was one by the clock tower on Lewisham high street when I was a kid and I can remember watching it very carefully whenever we went there shopping, in case the Doctor stepped out of it. I imagine that admitting that the Doctor I was thinking about was the Patrick Troughton incarnation may well age me even more.
It has been said that your first Doctor is like your first love; you never forget and good though the others may be, thay have to do a great deal to eclipse the first. Personally, I take that with a pinch of salt, as much fondness as I might have for the Troughton years, I have to say that there were better periods in the programme's history.
At it's best, Doctor Who managed to combine a genuine sense of peril with a sense of fun that appealed to children of all ages. Hard SF it isn't and never has been; it was Poul Anderson who gave a very good argument for considering anything involving time travel as fantasy and not SF, though I have to admit I haven't the faintest idea what that argument was. All I remember was that it impressed me greatly when I read it.
For me, the real issue is whether the "New Who" holds true to the spirit of the old or not. I'll leave debates of whether there's only one other incarnation left or not to the continuity nazis as, frankly, such things are beside the point. From its earliest beginnings, the show made it up as it went along. The whole reincarnation thing was a masterstroke of invention produced to conveniently explain changing Hartnell for Troughton. Later, to explain the Master's decrepit appearance in The Deadly Assassin the idea of twelve incarnations was invented. I see no reason why the programme should not just quietly ignore this or pull out one of the dei ex machinae of which the modern form of the show is so fond to explain this away.
If the idea of this raises your hackles, well remember that the daleks were utterly destroyed in their very first storyline and yet were able to return when children all over Britain took to wandering around school playgrounds with cardboard boxes on their heads grating in mechanical voices, "exterminate". Likewise, the cybermen somehow found a way back from final death in their first adventure to return and then from a different home planet, from Telos, rather than Mondas. The programme makers feel free to reinvent the history of the show as they need to to make it relevant and enjoyable to each generation and more power to them for doing so. It was only during the dark ages of the eighties and early nineties, when the hierarchy at Auntie Beeb decreed that the show had to be lighter and less scary that it lost its way.
In the "New Who" the show has returned to it's roots. It might have lost the multi-part format, it might have buggered with continuity and created all sorts of other issues with the possibility of hanky-panky in the Tardis (though admittedly, in my teenage years I would so readily have "done" Sarah Jane, Leela, Romana and one or two others and thought that the Doctor must have had superhuman self restraint not to have done the same) but in the end, it shares the same spirit as the original. And for that, I am glad.