An important milestone for building affordable robots that can become widely popular is to address robustly the simultaneous localization and mapping (SLAM) problem with inexpensive, off-the-shelf sensors, such as monocular cameras. These sensors, however, impose significant challenges on SLAM procedures because they provide only bearing data related to environmental landmarks. This paper starts by providing an extensive comparison of different techniques for bearing-only SLAM in terms of robustness under different noise models, landmark densities and robot paths. We have experimented in a simulated environment with a variety of existing online algorithms including Rao-Blackwellized particle filters (RB-PFs). Our experiments suggest that RB-PFs are more robust compared to other existing methods and run considerably faster. Nevertheless, their performance suffers in the presence of outliers. In order to overcome this limitation we proceed to propose an augmentation of RB-PFs with: (a) Gaussian sum filters for landmark initialization and (b) an online, unsupervised outlier rejection policy. This framework exhibits impressive robustness and efficiency even in the presence of outliers