We thoroughly investigate a simple model representative of the recently synthesized Janus particles, i.e., colloidal spherical particles whose surface is divided into two areas of different chemical composition. When the two surfaces are solvophilic and solvophobic, these particles constitute the simplest example of surfactants. The phase diagram includes a colloidal-poor (gas), colloidal-rich (liquid) demixing region, which is progressively suppressed by the insurgence of micelles, providing the first model in which micellization and phase separation are simultaneously observed. The coexistence curve is found to be negatively sloped in the temperature-pressure plane, suggesting that Janus particles can provide a colloidal system with anomalous thermodynamic behavior.