Rather than single out a particular Doctor (although I guess that the Fourth was "mine"), through the last few series of the re-booted outings (barring, oddly (and disappointingly), the last) I would cite Steven Moffat's stories as being exceptional.
Since it is being repeated (again) on iPlayer, I watched The Girl In The Fireplace (again); it's a story that I love because, despite the occasional logical flaws, I feel completely caught up in the emotion of it.
And it makes me weep like a small child.
Many reviews have cited various points which made them feel emotional, but no one seems to have pointed out my bit—the one that really clutches at me.
For me, it is the point at which the Doctor realises that the fireplace still links with the spaceship, 3000 years in the future: as he flicks the switch to activate the portal, he cries, "wish me luck!"
And Madame de Pompadour looks at him (at us) in desperation and, with a crack in her voice, simply says:
It's like any time that you have had to say goodbye to someone you love, knowing—somehow—that the relationship is done, or fundamentally changing: that something has been lost and, whilst you know that it must happen you wish that it would not. A last desperate cry to try to change an inevitable event which you wish—with all your heart—was not fixed.
And it gets me every time...