[Please note: I want to apologise for skipping over Demeter and Kore at the time I had allotted for Them. Sometimes I think I'll feel up for doing something, and then allergies or carpal tunnel syndrome, or whatever else goes wrong. I also must confess that I'm not the best at managing the time I have, in part cos I'm just too easily distracted.] 
Hesiod, Theogony 404 ff (trans. Evelyn-White) (Greek epic C8th or C7th B.C.) :
“Hekate whom Zeus the son of Kronos honoured above all. He gave her splendid gifts, to have a share of the earth and the unfruitful sea. She received honour also in starry heaven, and is honoured exceedingly by the deathless gods . . . For as many as were born of Gaia (Earth) and Ouranos (Heaven) [the Titanes] amongst all these she has her due portion. The son of Kronos [Zeus] did her no wrong nor took anything away of all that was her portion among the former Titan gods: but she holds, as the division was at the first from the beginning, privilege both in earth, and in heaven, and in sea. Also, because she is an only child, the goddess receives not less honour, but much more still, for Zeus honours her.”
I’ve found little about Hekate’s shrines specific to Boeotian traditions, but Hesiod apparently considered Her of great importance, and there is evidence that She was a widespread household goddess, with a a shrine at household gates, and at crossroads. At the deipnon (dark moon), the ancients left Her a meal, outdoors, as an offering. In Popular Wicca, She’s often cast as the “crone” aspect of the uniquely modern archetype on the “triple goddess”, while Demetre and Persephone occupy the “Mother” and “Maiden” faces.
Indeed, in Hellenic art, Hekate is consistently maiden, young woman, and Hekate Trimorphis is simply all Hekate. According to Pausanius, Hekate Trimorphis was first depicted in art as triple-headed or triple-bodied by the Attic artist Alkamenes, and came much later than the Triplicate imagery of Hekate that’s incredibly popular with Pop Wicca. I don’t reject Hekate Trimorphis images because they are “newer” and thus somehow not “proper recon”1. Indeed, if the only “correct” way to see Hekate is the oldest way, then She should be an invisible Goddess, appearing only as a glimpse of light from the corner of one’s eye, rather than the single-bodied maiden bearing torches. I don’t reject any image of Hekate, and though I see a more spiritual meaning of the epithet, I can see the value in portraying it literally.
She also had an important role in the cult of the Elusinian mysteries. She assisted Demetre in Her search for Persephone after Persephone was taken away to the kingdom of Hades. I’ve never had much interest in the Elusinian mysteries, so unless this changes, I’m going to leave any discussion of them to people who know more about it and have a better understanding of it than I do. 
One of the proposed etymologies of Her name is either giving origin to or coming from an obscure Lesbian epithet of Apollon, Hekatos, meaning “one that removes or drives off” or “far-darting one”. The most common offerings to Hekate in ancient times were to ward off evil spirits, as Hekate is the goddess of magic, witches, ghosts, and necromancy; She also is given messages to deceased loved ones. The pharmakis, or witch, Gale, was cursed by Hekate for moral incontinence and became the polecat, which some Hellenes kept as housepets for their vermin-catching abilities.
There really needs to be more imagery of Hekate with a lion and / or ferret.
The most common animal associated with Her is dogs, but I’ve always thought of lions when envisioning Hekate, and Theoi Project maintains a very brief sourced passage that one of Her forms is that of a lion, so I assume this personal association as Confirmed Gnosis, though probably not without help of cultural influences, including the English and U$ custom of statues of lions at the gates and doorways of important buildings and stately homes (or even just homes and estates that aspire toward stateliness).
1: …and for the record, it’s been AGES since I’ve seen some-one actually make such a ridiculous claim for rejecting a certain image or aspect or even deity, I even forget the name of the person who did it, but I also wouldn’t be surprised if other people continue to say it, and I just haven’t noticed.











