While perhaps not truly infinite, the DC Comics creations are all part of the same shared multiverse.
The Arrowverse first came into being during season 2 of Supergirl to be established as part of the same shared multiverse.
Please note that this is not a comprehensive list and that Earths which have been listed but not defined (such as the many numbered Earths on Jay Garrick's multiverse map) are not included. The following Earths have been specifically identified, either through the shows or associated media like the Crisis on Infinite Earths comic tie-in.
Earth-1
The setting of most of the Arrowverse shows, Earth-1 was said to be the center of the Arrowverse and the access point to every other Earth in existence. This was confirmed during Crisis on Infinite Earths, as Earth-1 was seen as the center of the multiverse and the last to fall to the Anti-Monitor's wave of anti-matter. It seems that the events which defined the other Earths were based around changes to the key events that occurred on Earth-1.
Earth-2
The first alternate Earth explored in detail, Earth-2 was also the Reverb and Deathstorm and Caitlin Snow being completely taken over by her Killer Frost persona.
Earth-3
Earth-3 was the homeworld of Jay Garrick; an older speedster who was also known as The Flash, whom mentored the Barry Allen of Earth-1. This Earth was somewhat old-fashioned, having a level of technology comparable to the 1930s. Gangsters still used Tommy guns and zeppelins were a popular mode of transportation. The villains were also decidedly goofier, with The Flash's arch-enemy being a version of The Trickster who resembled the classic Joker.
Earth-9
The opening of "Crisis on Infinite Earths - Part 1" revealed that Earth-9 was the home of DC Universe's Doom Patrol, is set on the same Earth. Either way, it was clearly Titans' versions of Hawk and the Jason Todd Robin who were vaporized during the Monitor's opening monologue.
Earth-12
Home to Nihilist scientist Harrison Wolfgang Wells, little was known about Earth-12 beyond it being a scientifically advanced world and its version of Harrison Wells being inexplicably German. We know it had an active publishing industry, as Wolfgang became a best-selling author after writing a guide to his philosophy, Everything Is Meaningless, So Why Did I Buy This Book? Earth-12 was also depicted as being advanced enough for inter-dimensional communication to be fairly commonplace and Wolfgang was shown to be in frequent with other versions of himself from around the Arrowverse.
Earth-13
Earth-13 was a world where the laws of magic reign supreme over science, and elves and dragons still live alongside humans. Most of what we know of Earth-13 was revealed by the wizard Wells The Grey in one posting on the Chronicles of Cisco blog. For his part, the Cisco of Earth-1 believed that the Wells of Earth-13 was a crazed Lord of the Rings fanboy whose love of the halfling's leaf had clearly slowed his mind. Of course, Cisco may have been biased, as Wells the Grey's description of Earth-13 spoke of a race of humble furry-footed folk called Ciscos.
Earth-15
Earth-15 was a dead world, notable only for its being completely uninhabited. This was due to an undefined disaster in 1986, which left it a barren wasteland. Cisco Ramon used his Vibe powers to dispose of various dangers safely on Earth-15, most notably using it as a venting ground for the excess radiation generated by the metahuman called Fallout in "The Trial of The Flash."
Related: How The Flash Died In The Crisis On Infinite Earths Comic
Earth-16
Revealed as an alternate Earth rather than a potential future of Earth-1, the Legends of Tomorrow once traveled to the future of Earth-16 and helped their version of Flashpoint.
Earth-17
Another Earth whose existence was revealed through communication with an alternate version of Harrison Wells, Earth-17 seemed to be a world of advanced scientific achievement. Its version of Harrison Wells (who spoke with a Received Pronunciation British accent) was one of the few people intelligent enough to crack the cryptogram devised by Harry Wells of Earth-2 as a means of testing replacements for his position on Team Flash. This Harrison Wells also wore a top hat with goggles, suggesting that Earth-17 had a similar Steampunk aesthetic.
Earth-18
First seen in "Lazarus Pits in the multiverse. This version of Hex lacked the famous facial scars possessed by the Jonah Hex Sara knew from her adventures traveling through time. Sadly, his face did not remain pristine after a fight with the two women.
