From a papyrus containing magical incantations:
For those possessed by demons, an approved charm by Pibechis:

Take oil made from unripe olives, together with the plant mastigia and lotus pith, and boil it with marjoram (very colorless), saying, “Joel, Ossarthiomi, Emori, Theochipsoith, Sithemeoch, Sothe, Joe, Mimipsothiooph, Phersothi, Aeeioyo, Joe, Eochariphtha: Come out of such a one”—and the other usual formulae.

But write this phylactery upon a little sheet of tin: “Jaeo, Abraothioch, Phtha, Mesentiniao, Pheoch, Jaeo, Charsoc,” and hang it round the sufferer. It is of every demon a thing to be trembled at, which he fears.
A letter from husband to wife:
Hilarion to his sister [=wife] Alis, very many greetings; likewise to my lady Berous, and Apollonarion:

Know that we are still in Alexandria. Do not be anxious; if they really go home, I will remain in Alexandria. I beg and entreat you, take care of the little one, and as soon as we receive our pay, I will send it up to you. If by chance you bear a child, if it is a boy, let it be, if it is a girl, cast it out.

You have said to Aphrodisias, “Do not forget me.” How can I forget you? I beg you, then, not to be anxious.
Greek Mysticism
A notable man of letters (Aelius Aristides) describes his encounter with the god Asclepius:
For there was a feeling as if taking hold of him [the god] and of clearly perceiving that he himself had come, of being midway between sleeping and waking, of wanting to look, of struggling against his departure too soon, of having applied one’s ears and of hearing some things as in a dream … hair stood straight; tears flowed in joy; the burden of understanding seemed light.

What man is able to put these things into words? Yet if he is one of those who have undergone initiation [into a Greek religion], he knows and is familiar with them.
Nature Religion
From a letter by the stoic philosopher Seneca (died A.D. 41):
If you have ever come on a dense wood of ancient trees that have risen to an exceptional height, shutting out all sight of the sky with one thick screen of branches upon another—the loftiness of the forest, the seclusion of the spot, your sense of wonderment at finding so deep and unbroken a gloom out of doors, will persuade you of the presence of a deity.

Any cave in which the rocks have been eroded deep into the mountain resting on it, its hollowing out into a cavern of impressive extent not produced by the labors of men but the result of processes of nature, will strike into your soul some inkling of the divine.

We venerate the sources of important streams. Places where a mighty river bursts suddenly from hiding are provided with altars. Hot springs are objects of worship. The darkness or unfathomable depth of pools has made their waters sacred.

And if you come across a man who is never alarmed by dangers, never affected by cravings, happy in adversity, calm in the midst of storm, viewing mankind from a higher level and the gods from their own—is it not likely that a feeling will find its way into you, [a feeling] of veneration for him?… Into that body there has descended a divine power.