This answer is specific to the original Dune canon. There are very few mentions of Earth, but I believe this answer collects all of them.
Characters with Other Memory have recollections of Earth, but these are mostly lines about their remembering, and not about what they remember. All explicit mentions of what they remember refer to things from pre-space history (that is, real, out-of-universe history).
Earth is still in existence following the Butlerian Jihad. The Commission of Ecumenical Translators spent 7 years on Earth writing the Orange Catholic Bible.
C.E.T. convened on a neutral island of Old Earth, spawning ground of the mother religions.
The Butlerian Jihad concluded in 108 BG, but there are no dates associated with the Orange Catholic Bible. The Guild existed at the time of the C.E.T., but was said to be beginning to build its monopoly, and the dating system B.G. is listed as being based on the "genesis" of its monopoly. So it is open to interpretation as to how long the Guild existed "Before Guild".
Earth likely still existed at the time of Arrakis's original colonization. There are several mentions in Dune about life from Terra that was brought to Arrakis when it was initially terraformed. It could be argued that these species may have originated on Earth, but could have been introduced to other planets first, and then brought to Arrakis later on.
KULON: wild ass of Terra's Asiatic steppes adapted for Arrakis.
Two characters own items from Earth. Darwi Odrade owns an original Van Gogh painting, which is mentioned frequently in Heretics and Chapterhouse. In Dune Messiah, Paul briefly picks up and puts down a conch shell:
The remains of a conch shell from the seas of Mother Earth lay on a low table beside the balcony rail.
However, both of these characters have access to immeasurable wealth (as Emperor and post-Empire Mother Superior), and possess Other Memory.
The most we know about Earth's existence at the time of the novels has to be derived from this exchange between Paul, Korba, and Stilgar in Dune Messiah:
[Stilgar:]"M'Lord, I can name every world our people touched in their migrations. I know the reaches of Imperial . . ."
[Paul:]"The Golden Age of Earth, have you ever studied that?"
"Earth? Golden Age?"
Stilgar was irritated and puzzled. Why would Paul wish to discuss myths from the dawn of time?
"Stilgar," Paul said, "you urgently need a sense of balance which can come only from an understanding of long-term effects. What little information we have about the old times, the pittance of data which the Butlerians left us, Korba has brought it for you. Start with the Genghis Khan."
The Golden Age of Earth is mentioned earlier in the book: Scytale wonders if Farok (a Fedaykin) has ever heard of camels or the Golden Age of Earth. We can't tell much from Scytale's knowledge of this though, since he is Bene Tlielax (and can be loosely considered as belonging to the Other Memory category).
It's not clear if Stilgar actually knows what the Golden Age is, but either way, he considers either Earth or its Golden Age to be myth. Paul then informs us that the Butlerian Jihad caused large amounts of history to be lost. Maybe this came just from losing all computer archives, or maybe it was direct destruction of historical records, as Leto II himself would later do.
Let's jump back to writing of the Orange Catholic Bible by the C.E.T.. Take note of these lines, all taken from the same section:
Mankind's movement through deep space placed a unique stamp on religion during the one hundred and ten centuries that preceded the Butlerian Jihad.
Immediately, space gave a different flavor and sense to ideas of Creation. That difference is seen even in the highest religious achievements of the period. All through religion, the feeling of the sacred was touched by anarchy from the outer dark. [...] During this period, it was said that Genesis was reinterpreted, permitting God to say: "Increase and multiply, and fill the universe, and subdue it, and rule over all manner of strange beasts and living creatures in the infinite airs, on the infinite earths and beneath them."
They met "in the common belief that there exists a Divine Essence in the universe." Every faith with more than a million followers was represented, and they reached a surprisingly immediate agreement on the statement of their common goal:
"We are here to remove a primary weapon from the hands of disputant religions. That weapon -- the claim to possession of the one and only revelation."
I think that these lines, along with the exchange about the Golden Age of Earth, tell us everything we need to know about Earth's role at the time of Dune.
Humans had been colonizing the universe for 11,000 years prior to the Butlerian Jihad. Space travel complicated the old ideas about religion. The Butlerian Jihad, which was religious in nature and caused a great loss of historical records. Earth was still considered the source of all religions at this time. All major religions convened on Earth following the Jihad, and mutually agreed to believe the universe itself was divine, and there was no one true revelation. 10,000 years go by, and the Orange Catholic Bible has remained.
Through both intentional & accidental action, Earth lost its status as religiously significant. By 10,000 AG, it is no longer known, believed, or important that Earth is the origin of humankind. Unless you have Other Memory and know better, Earth just really isn't worth mentioning.