That inverse square root algorithm is a neat trick, but it did not revolutionize anything.<p>In addition to several algorithms already mentioned, I feel that suffix trees and suffix array algorithms should be there as well. They are making all kinds of approximate searches feasible in bioinformatics.
I can't fathom why the Simplex algorithm wasn't included, it's considered, with reason, the most important algorithm of the 19th century.
I'm not sure you can call the Euclidean algorithm a "computer algorithm", it having been discovered some 2,000 years before computers existed.
Let me add: Least Angle Regression.<p>It's an efficient way for performing Lasso (L^1-penalization) to regression models, which has the benefit of (in addition to reducing risk of overfitting) producing sparse models.