The increase in the frequency of use of the Internet causes the attacks on computer networks to increase. Such phenomena also increase the importance of intrusion detection systems. In this paper, KDD Cup 99 dataset is used for the classification of the network attacks. Four different classification algorithms were used, and the results were compared. These algorithms were multilayer perceptron network, decision trees, fuzzy unordered rule induction algorithm (FURIA) and support vector machines. The most successful algorithm in this dataset found as FURIA. As the second part of this study, the most important feature sets were found by correlation-based feature selection and best first search algorithm. Then, the results of classification algorithms were compared with these new feature sets according to the performance of the algorithms.