I will be the first to confess I don’t give a great deal of personal attention to heroes, despite the fact that in Hellenic religion hero cults were fairly popular. Once in a great while I will give a nod to Herakles, and I do observe some of the major Athenian festivals focused on Theseus. But most of the big name heroes I don’t do much for on a personal level. This is to say I don’t have favorites, but those heroes I admire don’t always result in regular cultus being paid to them.
A significant part of the problem may be because I don’t feel any relativity of the heroes in my daily life. I can appreciate the spiritual allegories served in many of their myths (for which I have taken part in some of the major festivities), but on a personal level there lacks a connection. It was different of course if it is a local hero. I imagine that in ancient Hellas the heroes of one’s city state were nearly seen as ancestrial figures because they were so positively connected to one’s homeland. Therefore there was a premade condition of connection with the hero based on geography. For those of us living outside of Hellas this can be problematic. Of course there are heroes like Herakles who were widespread Heroes and took part in many city-states over the course of his myths. In fact, Herakles of all the heroes is the one who really got around and is therefore perhaps the most tangible to worshipers of various backgrounds, and tends to be one hero was more or less universally appreciated throughout Hellas. Another widespread hero, or rather pair of heroes, at least through the Peloponnese, were the Dioskouri, who served not only as protective household gods of the roof, but also important civic heroes.
Now among heroes it seems that we have different classes, and what kind of hero they were likely played a great part in how they were honored. On one hand you have heroes who do great deeds, such as Persues (a personal favorite), Jason (another big time personal favorite), Bellerophon, Achilles, Herakles, Theseus, Atalanta, Cadmus, Triptolemus, Crecrops, Sarpedon etc. Then you have the (usually prematurely slain) children of the gods, many of whom were beneficial in some fashion to mankind either before or after the death: Local mythical city founders are a big one, such as Delphus, but then you also have heroes such as Achilles (again), Asklepios, Orpheus, Teneros, Trophonios, Aristaios etc . And then there are the souls who are loved by the gods and are immortalized, usually either after being kidnapped to dwell with the gods or the souls carried up among the gods followin death: Endymion, Kyrene, Hyakinthos, Ganymedes, Adonis etc
I would have to say that other than my less regular observances for my favorite heroes, perhaps the most regularly honored heroes in my household are Kyrene and Hyakinthos, and three sons of Apollon (Trophonios, Asklepios and Aristaios). Although I have been thinking of honoring Jason more regularly as well if can figure out just how I want to do it and how regularly I wish to do it. As well as what benefit could be understood from honoring Jason….because each hero often has a different cultic focus depending on the hero. Sometimes it is just a sense of cultural kinship as in the case of Ion for the Athenians, and Hyakinthos for the Spartans. Other times it is very specific purpose of honoring, such as for Asklepios being petitioned for healing, or Trophonios as an ocular divine hero. And other times, such as my purpose for honoring Kyrene, it is symbolic of some tie to a specific god and a connection you are nurturing with them by additionally giving honor to that hero or heroine.
So there is an importance to giving reverence to heroes, and it is something that is often overlooked. Something I am quite guilty of myself to be honest.