My list -
Sklansky - Theory of Poker. Will cover basic (well, basic for poker) concepts, math, and strategies of the game. Builds up the chops for the real learning to come.
Second, get super sysstem 2 and read it cover to cover. You do not have to pick up every game, but you should read all of it to get the overall feel for the skills required to play poker. When finished, reread the NL section as it is the standard from which all others will be compaired.
Now we are ready to actually learn about specific games. Lets start with tournament NL holdem.
Harrington on Holdem V1 and 2. Not much else to read. Therse are the best books ever written on tournament play.
Limit Holdem:
I will assume that you will be starting at the lower limits and working your way up.
Low Limit Holdem - Lee Jones. This is a good beginner book for playing low limit games. We gotta start somewhere.
Small Stakes Holdem - Millet, et all. Builds on the concepts started in Jones book.
Holdem for Advanced Players - Sklansky, one of the best works on the limit game
If you are interested in Hi-Low split games
High-Low-Split Poker, Seven-Card Stud and Omaha Eight-or-better for Advanced players, Ray Zee. This is to O8 and Stud8 what supersystem is to NL Holdem. The bible of hi/lo/
How to win at Omaha hi/low poker- Cappeletti
both are great books and cover different concepts well.
Genral non strategy books =
Tao of Poker
Mike Caro's tells book (or DVD if you can get a copy)
General reading - Card Player Magazine
While not my entire library, this will get you started in limit HE, NL HE, NL tournamnets, and Omaha8 (or Stud

.
Perhaps the best reading advice that I cold give would be to take the contents of each book, and use it to formulate your own game. If you play strictly "by the book" strategy (like playing strictly off of the hand charts in HFAP), you will probably be able to beat the lower limits, but will not be able to beat better players when you try to move up. Adjustment is key.