This paper focuses on the problem of selecting relevant features extracted from human polysomnographic (PSG) signals to perform accurate sleep/wake stages classification. Extraction of various features from the electroencephalogram (EEG), the electro-oculogram (EOG) and the electromyogram (EMG) processed in the frequency and time domains was achieved using a database of 47 night sleep recordings obtained from healthy adults in laboratory settings. Multiple iterative feature selection and supervised classification methods were applied together with a systematic statistical assessment of the classification performances. Our results show that using a simple set of features such as relative EEG powers in five frequency bands yields an agreement of 71% with the whole database classification of two human experts. These performances are within the range of existing classification systems. The addition of features extracted from the EOG and EMG signals makes it possible to reach about 80% of agreement with the expert classification. The most significant improvement on classification accuracy is obtained on NREM sleep stage I, a stage of transition between sleep and wakefulness.