Errata are used for substantial errors in a paper, rather than mere spelling or grammatical errors. Citation of errata with original papers helps reduce error propagation in research. Unfortunately this is not as common a practice as it should be, mostly because authors are often unaware of an erratum, or believe that if they are aware of it, others will be too. The problem of error propagation due to failure to cite errata has been studied in the context of physics research by Thomsen and Resnik (1995). They find that the existence of an erratum does not decrease the citation frequency for the original paper, and the erratum is usually not cited with the original paper, allowing errors in research to propagate.
It is possible that this situation will improve now that most journals are online, owing to better online referencing of papers and direct connection of papers to their erratum. When you look at a paper from its original source in an online scholarly journal, it is usually obvious when there has been an erratum. However, it is still common for researchers to obtain papers from other sources where they are not alerted to this, and so this is not a panacea. (For example, some authors print out papers and then read from printed copies. If there is a later erratum, the researcher with a printed copy may have no idea that this has occurred.)
Though I am not aware of any formal "standard rules" on the matter, it is desirable to reduce error propagation in research, and so ideally it is best to always include citation of the erratum with the citation of the original paper. That way the reader is alerted to the existence of the erratum, and does not propagate any error in the paper. At a minimum the erratum should obviously be cited whenever the main citation to the paper touches on an aspect of the paper that is actually affected by that erratum (i.e., you should avoid error propagation yourself). But even in cases where the erratum does not affect parts of the paper that were of relevance to the main citation, it is also useful to cite the erratum in case an interested reader decides to read the cited paper in full, and is not aware that there has been an erratum. Evidently, from the fact that errata receive few citations, not many academics are doing this.
Speaking as someone who has published a mathematical paper with an error in an equation, and an erratum to correct that error, I would prefer it if all citations to my paper also cite the erratum with it, just to make sure that the original error does not propagate. It is not offensive to an author who has made an error to have the erratum to their paper cited; we are already aware we fucked up, and it is a relief when others do the right thing to minimise the damage.
Thomsen, M. and Resnik, D. (1995) The effectiveness of the erratum in avoiding error propagation in physics. Science and Engineering Ethics 1(3), pp. 231-240.