When they improvise, musicians typically alternate between several playing modes on their instruments. Guitarists in particular, alternate between modes such as octave playing, mixed chords and bass, chord comping, solo melodies, walking bass, etc. Robust musical interactive systems call for a precise detection of these playing modes in real-time. In this context, the accuracy of mode classification is critical because it underlies the design of the whole interaction taking place. In this paper, we present an accurate and robust playing mode classifier for guitar audio signals. Our classifier distinguishes between three modes routinely used in jazz improvisation: bass, solo melodic improvisation, and chords. Our method uses a supervised classification technique applied to a large corpus of training data, recorded with different guitars (electric, jazz, nylon-strings, electro-acoustic). We detail our method and experimental results over various data sets. We show in particular that the performance of our classifier is comparable to that of a MIDI-based classifier. We describe the application of the classifier to live interactive musical systems and discuss the limitations and possible extensions of this approach.