I have heard that with today's reversed phase HPLC columns, quality, reproducible separations are routinely possible without the use of buffers in the mobile phase and that buffers should be avoided whenever possible. This sounds to me like too broad a generalization and I question the validity of this statement. Can anyone provide some feedback?

I guarantee you that without pH control the reproducibility of your assay will suffer (assuming that your sample are acids and bases etc.)

Stop listening to who ever told you that buffers were unnecesary, at least in the case of separations that involve compounds that can be protonated, or unprotonated.

The difference in retention time of the fully protonated vs fully unprotonated form of a compound typically will be very large. (In the case of acids it may not even be possible to retain the anion form.) Where, in fact, the compound will elute between these extremes will depend on the ratio of protonated to unprotonated states. So,for selectivity as well as reproducibility, the ratio of protonated to unprotonated forms must be kept constant during the separation and the only way to do this is to buffer the mobile phase.

However, if the spearation is uneffected by pH then there is no need to buffer and one shouldn't.

For chromatographing a weakly basic compound, couldn't one simply acidify the mobile phase such that you are well below the pKa of the compound rather than use a buffer salt?

In principle yes. But you must be sure that you do not get an only partial ionization. In the case of a weak base, its pKa will shift towards a lower pH in the presence of the organic solvent.