AdaBoost
Freund and Schapire showed how to combine classifiers barely better than chance into one strong classifier, raising the weight of mistakes at each step.
Why it matters
The theoretical question of whether a weak learner can be made strong got a practical answer, and it immediately started winning competitions.
Each successive classifier trains on a reweighted sample where examples the earlier ones got wrong count for more. Training error falls exponentially with the number of steps. The method proved oddly resistant to overfitting, which stayed a theoretical puzzle for years. In 2001 the first practical face detector was built on AdaBoost.