I have all of the Tom Baker and Peter Davidson episodes on BETA. Take that!
Here's some basic info for you. The BBC serial (that means episodic) began in the 60s, in black and white. The Doctor is a Time Lord who travels through time and space in his craft, the TARDIS (Time and Relative Dimensions in Space). He usually has at least one assistant with him, and it's usually a pretty girl. A Tardis can change shape to mimic anything, thus helping it blend in when it visits a new enviornment, but the chameleon circuit in the Doctor's Tardis is broken, so his Tardis always looks like a Police box.
A Time lord can regenerate 12 times -- instead of dying, he/she gets a new body. (Easy way to excuse the switching out of actors as the series progressed.) The Doctor's nemesis is The Master, an evil time lord.
In the new series, the Doctor is the last Time Lord (though the Master makes an appearance in a few eps).
In previous iterations of the series, the Doctor traveled to new planets in every episode, but the newer shows take place almost entirely on Earth. (Way to keep the budget down, I should think.) Torchwood is an organization created to help protect Earth from aliens. Spun off into its own (also excellent) show.