The paradox of apparent optical associations of galaxies with very different redshifts, the so-called anomalous redshift problem, is around 35 years old, but is still without a clear solution and is surprisingly ignored by most of the astronomical community. Statistical correlations among the positions of these galaxies have been pointed out by several authors. Gravitational lensing by dark matter has been proposed as the cause of these correlations, although this seems to be insufficient to explain them and does not work at all for correlations with the brightest and nearest galaxies. Some of these cases may be just fortuitous associations in which background objects are close in the sky to a foreground galaxy, although the statistical mean correlations remain to be explained and some lone objects have very small probabilities of being a projection of background objects. The sample of discordant redshift associations given in Arp's atlas is indeed quite large, and most of the objects remain to be analysed thoroughly. For about 5 years, we have been running a project to observe some of these cases in detail, and some new anomalies have been added to those already known; For instance, in some exotic configurations such as NGC 7603 or NEQ3, which can even show bridges connecting four object with very different redshifts, and the probability for this to be a projection of background sources is very low. Not only QSOs but also emission-line galaxies in general are found to take part in this kind of event. Other cases are analyzed: MCG 7-25-46, GC 0248+30, B2 1637+29, VV172 and Stephan's Quintet and, in some of them, it is probable that the associations stem from a background projection, although some other low probability features are present in some of these systems which remain to be understood.