10. Recognition in popular culture
Quite often, whenever Doctor Who is referenced in a TV show or a movie, that reference will be one of three things. It could be the Daleks, due to being the most recognizable monster. It could be the current Doctor, to establish that the writers know their stuff. Or, perhaps most likely of all, it could be the Fourth Doctor. Maybe other past Doctors could be referenced, but generally speaking, it's the Fourth Doctor that gets referenced the most.
Perhaps the most amazing thing is that this isn't just limited to TV shows or films made in the UK, where Doctor Who is a national institution. You'd also see the Fourth Doctor pop up in US shows like The Simpsons, Futurama, and Family Guy.
If a geeky character has to dress up as one of the Doctors, more often than not, it's the Fourth. Even in shows like The Big Bang Theory or Criminal Minds, characters like Sheldon Cooper or Spencer Reid enjoy dressing up as the Fourth Doctor rather than anyone current.
Out of all of the many Doctors, why is the Fourth the most referenced? There are multiple reasons for this, which I'll get to. But because he is referenced so much, it's helped ensure that even today, the Fourth Doctor is instantly recognizable, both to fans and non-fans alike.