Given what is known of the percentage of women in antiquity who could both read and write it is likely that much of Sappho's influence derives from oral transmission among women. It is impossible now to know how extensive her influence was in that regard. The most likely example of that sort of influence is Song of Songs, which itself appears to have been initially an orally composed/performed poem or anthology of poems that made its way into the Old Testament through the backdoor, so to speak. I have created a separate file identifying language in the Greek version of Songs 5:2-6 that would have been perceived as echoes of Sappho by an educated woman in antiquity (eg, Poppaea Sabina, the Jewish wife of Nero). This issue has importance independent of whether or not such echoes should be deemed evidence of Sappho's influence on the author/translator of Songs.
Another way Sappho may have influenced oral 'literature' relates to what has commonly been translated as 'matchmaking' as practiced, for example, by the mother of Socrates, Phaenarete. My hunch is that matchmaking assessments would have been poetic/prophetic and substantively related to epithalamia and hence Song of Songs. The fragments of Sappho's epithalamia have assessments of both the bride and groom. Here is an analysis of what Socrates has to say about his mother's medical practice that included 'matchmaking.'
'Non-religious' ancient Western literature: (by 'non-religious' I mean from a modern perspective--obviously a poem such as the Homeric Hymn to Aphrodite was 'religious' from Sappho's perspective, not to mention other poems and works of art).
* Homer: See my discussion of the similarity of S. 44 and Iliad 22.466ff; the similarities may reflect Homer's influence on Sappho--or vice versa--or each reflecting a common tradition (the same issue applies to the Homeric Hymn to Aphrodite).
* The Homeric Hymn to Aphrodite: A translation of this Hymn is here. The possible influence of Sappho on it relates primarily to the poem by Sappho discovered in 2004, S. 58b.
* Anacreon: the earliest definitive evidence of Sappho's influence (apart from Alcaeus) is Anacreon 358.
* Mythology: Sappho is one of the earliest (in one case the earliest) authors to refer to myths that became important in later ancient literature (and then modern literature). Aphrodite & Adonis (See S.140); Medea (S.186).
* Wedding Songs (including Song of Songs): Sappho's influence on this genre in ancient times was enormous. Here is a link to an unpublished dissertation on the topic of Greek wedding songs by Toni Badnall (formerly at Oxford) with much that is directly relevant to Sappho. Also see below on Sophocles, Antigone.
* Sophocles, Antigone: Line 800 (Chorus): the reference to Aphrodite as 'amachos' is clearly an echo of S. 130 (the adjective is a cognate of the one Sappho uses to characterize Eros). This should not be as surprising as it might otherwise seem as the entire play Antigone is a kind of funereal wedding song and surely has many more echos of Sappho that can be spotted today given how little of her poetry survives. The genre of funereal wedding songs is significant: Romeo & Juliet is the most famous example in English.
* Plato: although it is only an inference, there is a passage in Phaedrus where Plato appears to paraphrase a poem by Sappho (251a-252a); the rural setting (230b-c) may have been inspired by S.2. The medical theory attributed to Hippocrates (270b-d) arguably relates to Gorgias and his theory of poetry that was perhaps inspired by Sappho (see S.16). Not only is that one of Plato's most influential dialogues, the passage in question was especially important to the Neo-Platonic/Pythagorean tradition of late antiquity (see below for more); because of the direct or indirect influence of Phaedrus on the composition or interpretation of Song of Songs the importance of Sappho's connection to this dialogue is impossible to overstate.
* Theocritus: S. 2 is clearly being echoed in Idyll 7 (Harvest Festival). Idyll 7 has been especially popular. Heidegger, for example, quotes it in his travelogue of his last visit to Greece (discussed by Richard Capobianco here (p42ff)).
* Medical Literature (Hippocrates & Galen): For Hippocrates see S.120 and my discussion of Gorgias in my comments to S.16; for Galen see S.50.
* Lucretius: 'te sociam studeo' (De Rerum Natura 1.24) is as plainly an echo of Sappho (S.1.28) as anything in ancient or modern literature. Noted by E. A. Hahn, how it has otherwise escaped the attention of scholarship on either Sappho or Lucretius is beyond me to explain.
* Catullus--and not just his own version of S. 31, but his longer poems C. 61-4.
* Vergil: his famous 4th 'eclogue,' which is in fact an epithalamium, clearly echoes Catullus in places and may reflect Sappho's influence in ways that cannot now be detected with certainty.
* Moretum: Long attributed to Vergil but then gradually assumed to be by someone else: I have become convinced this poem is the composition of a woman. The detectable echoes of Sappho in it are at best very faint. Yet if this is a poem by a woman there is surely much here that derives from Sappho directly or her influence on others. NOTE: I now have a separate sections focused solely on this poem (see the Black Goddess of Rome and the History and Importance of Taste).
* Horace: Here is a discussion of the influence, including a summary of a paper by Llewelyn Morgan on this topic. The basic takeaway is that because of the importance of Horace and the poem of his that appears to reflect influence of the 'Brothers Poem' the significance of Sappho's indirect influence on literature has increased substantially.
* Seneca (Medea (the epithalamium and in particular lines 92ff))
* Apuleius (the author of the story of Cupid & Psyche, a story that is the literary ancestor of such works as Beauty and the Beast). Apuleius is of special importance as evidence of Sappho's influence as he is the only author who mentions studying her poetry (complaining incidentally of her Aeolic Greek dialect that by his time was already arcane). Here is a post on Sappho's influence on Apuleius and its implications.
* Iamblichus, Proclus & Neo-Platonism/Pythagoreanism generally (more to come on this but for now see the letter to Iamblichus in the discussion of S. 48).
* Boethius (the poetry of the Consolation of Philosophy): an essay on this topic is here. This is intriguing because of Boethius's subsequent influence on Dante and Chaucer. But then there is also Hildegard von Bingen, who surely would have paid especially close attention to a text where a female 'Philosophy' teaches a man about cosmology, using, inter alia, poetry (on this also see the discussion of Moretum). And of course then there is Queen Elizabeth I. Jantzen in Foundations of Violence sees Boethius as but part of a tradition of male appropriation of the female voice; on this and on Parmenides I respectfully but strongly disagree.
Sappho's Influence on Judaeo-Christian Literature:
Here is a link to a discussion of the most important issues.
Because of Sappho's influence on Plato's Phaedrus and Song of Songs tracing her direct or indirect influence is very difficult. A particularly intriguing example of this is the way some of what is attributed to Mecht(h)ild of Magdeburg (MM) resonates with some of Sappho's poetry--notwithstanding that she surely knew no Greek (she did not even know Latin) not to mention that there is no evidence of any manuscript containing any of her poetry circulated in Germany in the 1200s CE. See the excerpts Martin Buber included in Ecstatic Confessions on p59-60 (compare MM's diagnosis of her soul's love sickness for God to S. 31 and compare God's response about awaiting her in the garden of love cf. S. 2 (a poem first discovered and published in the 20th century (albeit echoed by Gregory of Nazianzus in a text to which MM may have had access)).
Sappho's Possible Influence on Buddhist Literature & Practice:
This is very speculative and unlikely ever to be substantiated to a significant degree. The discovery of a statuette of Aphrodite in the early 20th century near what is now the US Bagram Air Base in Afghanistan may indicate interest in Greek female spirituality around the time and in the region that Tantric elements of Buddhism were beginning to emerge. By contrast with the physical trade in artifacts that likely best explains the presence of such a statuette in an ancient Afghan storehouse of some type, it is relatively easy to imagine Sappho's poetry (that there is solid evidence was often memorized in antiquity) could have made it there. See my discussion of S.105 and S.1.
Sappho's Influence on Modern Literature:
* Albrecht Dürer: Of course Dürer is primarily considered an artist, but his work straddles several categories because of how it leveraged off of what was then the revolutionary technology of printing. I have a short essay that relates to how one of his engraving/drawings (absurdly characterized as 'four witches') reflects the influence of ancient Greek female spirituality on him and hence how he became a vital conduit by which that spirituality was transmitted, for example, to Caroline Schelling.
* Shakespeare: his earliest publication, Venus and Adonis derived from at least one ancient source (Bion) that likely was borrowing from Sappho. The balcony scene from Romeo and Juliet seems to have an indirect echo of S. 31 and possibly another from a wedding song by Sappho. For more granularity on this go here. Also see the very likely echo of Sappho in Antigone and the relationship of the death scene of Romeo and Juliet to the narration of the deaths of Antigone and Haemon in Antigone.
* Aemilia Bassano Lanier: how much (if any) direct influence Sappho may have had on this female poet is unclear to me. There are many intermediary sources to consider: Song of Songs and the poetizing female Philosophy of Boethius's Consolation of Philosophy (that was especially influential in England due to its early translation by Alfred the Great and then another done by Queen Elizabeth). This blog post on her is worth a read.
* Caroline Schelling: There are two echoes of Sappho (one from S. 31and one from S. 1) in the 4th Letter of Caroline that survives, a letter she wrote October 7, 1778 when she had just turned 15. I see no specific mention of Sappho in her letters but there is no question but that Caroline would have known her poetry in translation (not only did she grow up in a town that was home to one of the most prestigious universities in the world but she was she the daughter of a prominent philologist and had a friend who was the daughter of another prominent philologist (Heyne)). I have been doing a lot of research on Caroline and will post links here and elsewhere on this blog to what I am writing based on that research.
* The American poet H.D.: Assessing the influence of Sappho on her (and accordingly the indirect influence of Sappho through H.D. on others) necessitates being sensitive to what H.D. (who did study ancient Greek) actually knew of Sappho (which was considerably less than is known today).
* A. E. Housman: this is no surprise given Housman was an excellent Classics scholar in addition to being a poet. Epithalamium (Last Poems XXIV) in particular is inspired by S.104a as well as other fragments of Sappho's wedding songs. The inspiration probably also relates to Housman's interest in the Latin astrological poet Manilius, for S.104a appears to be itself an astrological poem.
* Anna Akhmatova: as with H.D. the influence of Sappho on Akhmatova and other early 20th century Russians needs to be assessed against the prevailing views on, and available translations of, Sappho. I have a short essay comparing the New Sappho to the Old Akhmatova here.