Tom Baker was the Doctor longer than anyone else has been so far, and at this stage it's hard to imagine anyone surpassing him (although you never know- maybe Matt Smith will stick with it until he's David Tennant's age). His appearance is certainly the most iconic: the curly hair, the hat, the world's longest scarf, the great big teeth. He combined the endearing clownishness of the Second Doctor with the derring-do of the Third.
The Fourth Doctor is frequently discussed as more alien than his predecessors. While his appearance is human, he is, let's be honest, an extraordinarily strange-looking man, and his clothing and behavior aren't exactly normal either. On the other hand, he often shows a very human range of emotions, such as when he doubts his right to commit genocide against the Daleks, or when he frolics across the streets of Paris with Romana.
The thing about the Fourth Doctor is that he was around for so long that it becomes hard to judge his tenure as one whole. Certainly there were moments of brilliance and wonder: the previously alluded-to "Genesis of the Daleks" and "City of Death," as well as "Pyramids of Mars," "Robots of Death," and "State of Decay," among others. On the other hand, there were some real duds, like "Revenge of the Cyberman" and "Meglos," in which the Doctor is impersonated by an evil cactus. No, really. If I wanted to make up the dumbest Doctor Who plot ever, I'm not sure I could do better.
Without going on too much of a tangent, I must mention that while I know it's well-regarded by fans, I have not been able to sit through "The Talons of Weng-Chiang." I understand that it's a product of its time and place, but I have a gut reaction against racist depictions of Chinese characters that I can't just turn off. Maybe I should try again, now that I have a blog in which to vent about the aspects that bug me.
The length of the Fourth Doctor's run also means he had a metric ton of companions, so I'll be even briefer than usual. Sarah Jane was awesome during her season with Pertwee, but she kind of becomes increasingly uninteresting as time goes on, with both her personality and her clothing taking a turn for the girlish and juvenile. A big part of her decline seems to be the addition of Harry Sullivan, who is such a pointless companion that he makes others less appealing in his presence. Leela is an odd fit, but has some great bits (double entendre accidental but endorsed). Romana I is a little too glamorous and haughty for me, but I do like how smart and confident she is. As for Romana II, if you didn't guess from that video, I adore her. She is, in my opinion, pretty much the perfect companion. It's just a shame she came along right before the 1980's started and everything began to suck. Speaking of which, then there was Adric, the Connor of Doctor Who. If they'd actually gone through with turning him into a vampire in "State of Decay," that might have made him an interesting companion.