I have to agree that Lou Malnati's is a sure-fire way to get an a fine exemplar of "classic" Chicago pizza. Uno's and Due's are the originators, but unless you're in the River North, it is seldom a convenient choice. I am surprised that there's been no love on this thread for Gino's East, which is very similar, and like Lou's, has several city and suburban locations.
Whatever you do, do NOT go into an "Uno Chicago Grill" and expect to get the original Chicago pizza recipe. In fact, don't go in at all, in my opinion. There's better to be had in many places.
The Stuffed variety of Chicago pizza is a little more mysterious and subject to a lot of variety. I'm fond of Edwardo's (although it doesn't seem as awesome as it used to since they stopped growing basil in the foyers), Giordano's, and Viccino's -- although the latter is only in the burbs.
What is patriotism, but the love of good things we ate in our childhood?
-- Lin Yutang