Classification algorithms are used to identify into which classes observations of data should fall. This problem could be considered part of pattern recognition in that we use training data (historical information) to recognize patterns to predict where new data should be categorized.
Fraudulent activity detection
Loan default prediction
Spam vs. ham
Benign vs. malignant tumor classification
and many more...
Logistic regression (both binomial and multiclass)
Linear Support Vector Machine
One-vs-Rest classifier (a.k.a. One-vs-All)