Off-the-cuff, i.e. without digging deeply into a set of history of statistics books:

Tied 1st place:

• Markov chain Monte Carlo (MCMC) and the Metropolis–Hastings algorithm

• Hidden Markov Models and the Viterbi algorithm for most probable sequence in linear time

• Vapnik–Chervonenkis theory of statistical learning (Vladimir Naumovich Vapnik & Alexey Chervonenkis) and SVMs

4th place:

• Edwin Jaynes: maximum entropy for constructing priors (borderline: 1957)

Honorable mentions:

• Breiman et al.'s CART (Classification and Regression Trees) algorithm (and Quinlan's C5.0 extension)

• Box–Jenkins method (autoregressive moving average (ARMA) / autoregressive integrated moving average (ARIMA) to find the best fit of a time-series model to past values of a time series)

(The beginning of the 20th century was much more fertile in comparison - Kolmogorov, Fisher, Gosset, Aitken, Cox, de Finetti, Kullback, the Pearsons, Spearman etc.)