How about some speculation for a beautiful early spring (or early fall depending on where you are ;-) day? The following is possibly heavily spoiler-laden, so highlight to read:

SPOILER
Count Dooku (Christopher Lee) was from the getgo being called a "charismatic separatist" in all the official literature. We've since found out that Dooku is one of the "Lost Twenty": twenty Jedi who split from the order. Dooku is the most recent, and according to our sources he left the Jedi soon after the death of Qui-Gon Jinn in TPM.

Here's the speculation of what could be Dooku's background: he was a noble, respected Jedi who took more than the Jedi's traditional passive role in the affairs of the Republic. Eventually he began seeing the growing corruption of the Republic's political system and stagnancy in the Jedi. He probably spent many years trying to work within the system, doing his best to effect real change but he only became more and more frustrated. Until finally there came a point where he felt he could no longer work within: he left the Jedi and separated himself from the Republic, and began attracting followers who were likewise disillusioned.

What would it take to bring Count Dooku to that point of divorcing himself from something he had trained for and served all his life? If he left so soon after Qui-Gon's death, only one possible answer so strongly presents itself: Qui-Gon Jinn was Count Dooku's apprentice.

The death of his Padawan might have been the final straw for Dooku. He would have angrily left and sought a quicker, easier path than the one the Jedi were taking. If Dooku is indeed Qui-Gon's old master, then the lightsaber duel between Anakin and Dooku later on in Episode 2 would eerily foreshadow Luke and Vader's fight in TESB: just as Luke could not have come into being without Vader, Anakin owes his training to Dooku, because if it ultimately weren't for Dooku, Anakin would not have been trained in the use of the Force!
END SPOILER

So what do you think? A possible parallel permutation in the saga? Feel free to discuss this concept here and post all of your ideas and speculation in the Jedi Council Forums.