Common Equestrian

Common Equestrian, or Common Language is the primary language spoken in Equestria and seems to also be the dominant language spoken in other realms, such as the Dragon Lands, Infernal Lands, Abyssinia, Changeling Kingdom, Thicket, etc.

History
The history of the language is thoroughly unclear. However, the oldest instance of the language may have been recorded during the post-Long Winter era of Equestrian history when Chancellor Puddinghead wrote down a recipe for pudding in what can be assumed to be the language, as was capable of understanding it.

Oldest known equine language
The earliest known possible variation of the Equestrian language was the "Cave language", the language spoken by the Cave ponies of years long ago. When Pinkie Pie and Applejack traveled back in time to the Stone Age, they were forced to deal with a Cave pony tribe. Pinkie Pie managed to, at least somewhat, understand their language and communicate with them, more-or-less befriending them and created the first ever party.

Old Northern Equestrian and Unicornian
When Rockhoof and Mistmane were teleported to the present age due to Dr. Hooves' time machine, they spoke Old Northern Equestrian and Unicornian language respectively.

Anugyptian
During the Anugyptian period of history, the Anygyptian writing system was practiced, though King Anubis and Queen Cleopatrot both still spoke the Common language. Their writing system was a hieroglyphic system that appeared to have elements of logographic systems too.

Olde Equestrianne
At some unknown period in history, the ponies of the Canterlot region spoke "Olde Equestrianne", a language that was also understood by Griffon merchants. The only known piece of writing in Olde Equestrianne was a bill that read that the Ponies burrowed Canterlot mountain from the Griffons, and they still owed them the Bits. However, this piece of information has been thoroughly retconned by, which showed that ponies even before the founding of Canterlot spoke the Common language.

In addition, literature writtne from the Age of Heroes was distinctly written in Common. While one could claim that Olde Equestrianne was just a dialect akin to Old English, it was noted in the story to be impossible to read unless one already knew the language, meaning it lacked mutual intelligibility

Old Equestrian
In earlier episodes, a script seemingly dated to the Age of Heroes was shown. It appeared to be a hieroglyphic or pictographic language of sorts, with several symbols based off images and iconography for everyday Equestrian life, such as horse heads, the moon, stars etc. Despite being alien in comparison to modern scripts, Twilight Sparkle could read it just fine. It's unknown if "Olde Equestrianne" was referring to this script or not, as Olde Equestrianne was never shown to the reader.

Modern age
In more modern times, a writing system resembling mroe of a free-form alphabetical script was formed. The oldest known piece of text written in this format was a recipe for pudding by Chancellor Puddinghead, though it was entirely possible the book was a recent translation of said text. The language itself is found on countless signs, in books and on other products.

IDW continuity
In the IDW continuity, perhaps to make it easier for the artists, the writing system of Equestria has consistency been depicted to be the Latin alphabet instead of the script used in the cartoon.

Basis
The idea of a "Common Language", although a historical one, is a recurring theme in several fantasy works. Other examples of common languages include in Middle-earth, and  in Star Wars. To us, the language may sound similar to English, but in-universe, it may sound much different. Or not, see below.

Writing inconsistencies
The Equestrian language has been subject to several inconsistencies due to its writing system. In some works, primarily comics and manga, the writing system is merely the Latin alphabet, while in others it appears to be a styalized evolution of the Latin script, which can be seen in the later episodes of the show. Sometimes the writing system appears to look almost like, which can usually be seen in in-universe books and scribes.

A similar thing appeared in My Little Pony Tales. In some episodes, such as "Birds of a Feather", the language was shown to be written much differently than English, but in others, it simply used the Latin script. See Ponyland language (Tales).

Existence of English
In the Human world equivalent of, English language exists, as Wallflower Blush mentions meeting Sunset Shimmer in 9th-Grade English.