Well, this is my first post to this wonderful site, and boy can I pick a forum!
While good points have been made on both sides, as a piano instructor, I have to say that exercises (particularly Czerny) are extremely valuable. As several have already posted, athletes rely on drills and sequential exercises to train the body. We pianists would do well to take heed and train our hands.
To answer Eddie's oft-repeated response that the same can be accomplished by playing songs, I disagree based on my personal experience and my experience with my students. The problem with using performance pieces to gain skill is that if you encounter a technical problem in learning the piece, the brain struggles to overcome that obstacle, and learning takes longer. Technical exercises are designed to sequentially build skill, fluidity, and accuracy, and, once mastered, allow my students to learn concert pieces more quickly and easily. I suppose if you wanted to struggle through song after song to build the full repertoire of skills, feel free. But why not build all of those skills in advance, and conquer complicated pieces more easily down the road. That seems to work for me, and it works wonders for my students!