There is no possible way I can pin down just one scene, so I had to pick a whole episode (albeit a seven minute one - but it still counts as an episode!)
When I first watched "Time Crash," I knew absolutely NOTHING about the Classic Series at all. I had seen pictures and fan art of the Classic Doctors, but I'd never seen any episodes. I was far from having a favorite Classic Doctor and I certainly could not remember all the names of the actors who had played the Doctor in the past. The most I knew was that a lot of people liked the Doctor with the scarf, but that was it.
Bearing all this in mind, when I watched this short episode and saw Ten bump into Five as they walked around the TARDIS console and the ensuing "What? What? WHAT?!" exchange, I knew IMMEDIATELY that this was going to be something special. Don't ask me why - I just knew. There are some dang funny lines in there - probably more than most regular episodes of "Doctor Who" (and they say Steven Moffat's main talent is writing scary stories) and it is just so much FUN! I am curious, though - when did the TARDIS have a leopard skin theme? (Noodle Incident, perhaps? If anyone can enlighten me on this, I'd appreciate it)
But the best part is the at the end with Ten's monologue to Five how he loved being Five and how awesome Five was (of course, this is fanboy!David Tennant - and, by extension, fanboy!Steven Moffat - speaking to Peter Davison, who is just awesome in his own right). When Ten said to Five "You were my Doctor," I really wanted to seek out episodes from the Fifth Doctor's time - Ten is my Doctor, so how cool would it be to watch your Doctor's Doctor? Plus, the mere fact an actor who played the Doctor way back when would come back and reprise the role briefly for the new series - that was endearing to me and that's part of why Peter Davison is my favorite of the Classic Doctors.
Also, speaking of brainy specs, this is a picture of me when I was three years old wearing glasses that I didn't need, but I wanted to wear them because I thought they made me look smart (they didn't have lenses in them)
(If that isn't proof that I was destined for geekdom greatness, I don't know what is).