I seem to be the first person to say this in reply to this particular Writer's Block question - and I hope to high heaven I won't be the last - but here we go:
Well, alright, technically the character's name is the Doctor, but if I say "Doctor Who" that distinguishes him from any other fictional Doctors on TV.
Why he made such an impact on me? Don't know. Right place, right time. I was five when I first became a fan of the show. It was fun, it was cheerful, there was this mad person travelling around time and space dragging his companions - and us along with him for the ride, defeating evil with a yoyo, a bag of jelly babies, and an impossibly long scarf. He's inspired me creatively in that he made me want to write - although I've not written (or at least not finished) many stories that are actually about him (one day...). And yes, I do collect lots of memorabilia, mainly books, magazines, DVDs, CDs, and (less so now) VHS tapes.
Watched Flesh and Stone earlier this morning. Brilliant stuff. The Doctor's still just as great as he was 35 years ago. Indeed, as he was 46½ years ago. Long may he continue.