The ability of an object classifier to adapt to new data and incorporate new classes on the fly is of paramount importance for robots operating in the real world. This paper presents an approach for incremental online learning of real-world objects to be used by robots operating in real environments. We combined the representational power of Convolutional Neural Networks with the adaptability features of Self-Organizing Incremental Neural Networks. We evaluated our approach on the RGB-D Object Dataset in terms of classification accuracy and incremental learning of new classes. Our results show that whereas our method does not yet compete with the performance of state-of-the-art batch learning algorithms, it offers the important advantage of being able to adapt to new data and incorporate new classes on the fly. Finally, we aim at establishing a baseline on a publicly available dataset for comparing different approaches to realize online incremental learning in the context of robotics.