I must admit up front that I haven't watched a huge amount of First Doctor episodes. I've seen "An Unearthly Child," "The Aztecs," and parts of "The Daleks." I've also seen "The Three Doctors," which he's barely in, and "The Five Doctors," in which he's played by a different actor.
Based on what I have seen, I like the original Doctor, but he's such a drastically different figure from the later ones that it's hard to even think of him as the same character. It seems like he was never meant to be the lead character in his own series- it's really more about Ian and Barbara (both of whom I pretty much can't stand), and sometimes Susan (who's cute but not very interesting either). The Doctor's purpose is just to be this enigma who takes them from place to place and time to time, and he pulls that off well. Also, I like what a jerk he is so much of the time. If nothing else, Ian totally deserves it. And in "The Three Doctors," when he calls Three and Two "a dandy and a clown," that's pretty great too.
First Doctor episodes I'm planning to watch soon: the rest of "The Daleks," "The Sensorites," "The Dalek Invasion of Earth," and "The Gunfighters." And yes, I've heard that last one is pretty awful, but I can't resist a western.