ROC-curves can be computed for several different types of discriminative classifiers.
Originally developed for analyzing radar blobs during the second world war (D. Green et al.(1966). Signal detection theory and psychophysics. Wiley), ROC-curves soon became applied in medicine.
First an individual medical test result was characterized by its ROC-curve. Take for example the measurement of hemoglobin in a patient, done by a lab in a hospital. Such tests are widely applied to diagnose anemia. In a peripheral hospital, the probability of a too low hemoglobin reading will differ compared with that of a specialized university hospital. The prior probability of anemia is different between the two types of hospitals because only a small fraction of the anemia patients cannot be diagnosed in the peripheral hospital. Only these difficult cases become referred to the specialized university hospital. A ROC-curve lets the lab persons characterize the discriminative ability of the hemoglobin test for different prior probabilities of anemia.
ROC-curves in machine learning
Machine learning adapted ROC-curves to characterize the discriminative performance of classifiers. Besides logistic and probit models, several other types of two-class classifiers can be evaluated using a ROC-curve. As long as the classifier outputs posterior probability estimates you can compute a ROC-curve by varying the discriminative threshold that discerns the two classes. Eligible classifiers are random forests, multilayer perceptrons with sigmoid activation units, the multinomial classifier, the probabilistic k-nearest neighbor classifier, the probability outcomes of insight classifiers, a probabilistic support vector machine, and even more types. Some machine learning suites like Weka offer ROC-analysis out-of-the-box.
The area under the ROC-curve is a measure of the total discriminative performance of a two-class classifier, for any given prior probability distribution. Note that a specific classifier can perform really well in one part of the ROC-curve but show a poor discriminative ability in a different part of the ROC-curve.