I'm a bit late to the party, and most of my favorites have already been well-represented:

Calvin & Hobbes - so empowering to a youngster with a good imagination.
The Far Side - introduced me into the more subtle side of humor (the Midvale School for the Gifted always comes to mind).
Non Sequitur - very intelligent.
Dilbert - love the cynicism and the cat.

But a couple of the best have not been mentioned:

Robotman - could be hit-or-miss, but when it hit, it was always a home run.
Life In Hell - the strip that got Matt Groening the chance to do The Simpsons, best satire ever.

There are also some great webcomics out there, for those that have never experienced them:

Scary Go Round - by a Brit (but it is still good ). Has an element of the old-style serial adventure comic, but also very funny. http://www.scarygoround.com/
Questionable Content - perhaps aimed at a younger crowd than AWADtalk, but very well polished in both art and humor. If you have time, check through the archives -- you can really see the author's skills improve over the run of the strip. http://www.questionablecontent.net
Diesel Sweeties - unique pixelated art, equally unique characters and stories. http://www.dieselsweeties.com
Dinosaur Comics - very unconventional strip that features the exact same art every day, with different text (read a few, you'll understand). http://www.qwantz.com
White Ninja Comics - quirky art and concept. Can be very Non Sequitur-esque. http://www.whiteninjacomics.com
Pathetic, Inc. - bizarre Photoshop-illustrated strip that could be called "Dilbert on speed and/or acid". Satan is a recurring character, if that tells you anything. If you check out today's, the back story is that these two office drones are trying to strike it rich with a homebrewed beer called Krep, and they have taken it to a contest in Germany. http://www.colintheriot.com/patheticinc