Naive Bayes is a very common classifier used for probabilistic multiclass classification. Given the feature vector, it uses the Bayes rule to predict the probability of each class. It's often applied to text classification since it's very effective with large and fat data (with many features) with a consistent a priori probability.

There are three kinds of Naive Bayes classifiers; each of them has strong assumptions (hypotheses) about the features. If you're dealing with real/continuous data, the Gaussian Naive Bayes classifier assumes that features are generated from a Gaussian process (that is, they are normally distributed). Alternatively, if you're dealing with an event model where events can be modelled with a multinomial distribution (in this case, features are counters or frequencies), you need to use the Multinomial Naive Bayes classifier. Finally, if all your features are independent and Boolean, and it is safe to assume that they're the realization of a Bernullian process...