Along with Big Apple, Sweet Apple Acres was going to be called Big Apple Orchard or Big Apple Farm - the idea was that Applejack's brother inherited the farm while she just ran things. It also was originally not supposed to be in Ponyville at all, but in a different town known as Fillydelphia.
The show was originally going to be named My Little Pony Adventures.
The show was originally intended to be 1/3 adventure stories, but it quickly became apparent that the extra workload they entailed meant they were difficult to pull off on the very tight production schedule. Lauren said that the main casualty of this was Zecora, with her originally planned mentor role not really needed.
Similarly, Lauren originally envisioned a lot more diversity in body types for the ponies, but that too would've been more work for the animators.
According to M.A. Larson, the Ponyville Schoolhouse's school paper was originally called The Horse's Mouth instead of Foal Free Press, and Featherweight was originally called Milquetoast and he was Namby-Pamby's little brother.
Several characters had name changes for legal reasons. Twilight Sparkle was Twilight Twinkle (a G3 pony), Princess Luna was Princess Selena, Apple Bloom was Appleseed, Big McIntosh was Big Apple, Gilda was Grizelda, and Zecora was Shaman.
In the original pitch, Apple Bloom was alone in her quest for a Cutie Mark. Lauren was asked to add in some friends to accompany her on her journey Thus, Sweetie Belle and Scootaloo and the Crusaders were born. Oddly enough, Lauren Faust always thought they should have their own Spin-Off show for preschoolers (where kids learn how to do stuff while the Crusaders are engaging in new activities looking for their cutie marks).
In Lauren's original pitch for the show, Pinkie Pie was a Pegasus Pony and Fluttershy was an Earth Pony. The entire cast went through a design change, from G1-style Ponies to G3-style Ponies (though some of them are In Name Only).
Lauren has said she had a sea ponies episode in mind, but it didn't get made under her watch. We almost got shoo-be-doo'd!
Trixie was originally going to be a boy, until the episode's scriptwriter suggested to Lauren to make the character female. Lauren admitted in an interview that this change was absolutely for the better.
Lauren originally designed several monsters to be cuter and prettier thinking Hasbro wouldn't let her get away with the monsters being "too scary". Turns out she was wrong and Hasbro didn't think her original designs were scary enough.
On the other end, the Ursa Major was much uglier and scarier before getting toned down (it's still pretty ugly and scary). Interestingly, in this case, the change was not due to worries that it might be too scary but because it the difference between adult and baby was too drastic and executives were worried that the intended demographic might not recognize the larger monster as being the same species.
According to Lauren, Rarity had a scene scripted for "Luna Eclipsed" where she goes overboard designing an outfit to soften Princess Luna's demeanor, leading to another humorous misunderstanding, but it apparently got cut for time, so Rarity is ultimately an Absentee Actor (though her voice actress is still present as Granny Smith and Luna).
There were plans for an episode centered around Big McIntosh. The episode was supposed to have little dialogue coming from the star character. However, it was dropped for a probable number of reasons (namely, that silence can get very boring).
According to Amy Keating Rogers, Derpy's scene in "The Last Roundup" was originally going to be a little longer, complete with a flashback on how the Town Hall got ruined. She was also named Ditzy-Doo (a character previously mentioned in "Winter Wrap Up" that Lauren Faust considered using Derpy's design for), but was referred to as "Derpy" at the director's request as a Fandom Nod. Considering what happened later, this nod probably was not the best idea (though certainly well-meaning).
Lauren said at a Bronycon panel that she originally proposed making Rarity the Element of Inspiration, but this was rejected for being too hard for kids to understand.
Lauren has said that she planned for a Scootaloo episode, which would have revealed that Scootaloo is disabled and would never be able to fly like the other Pegasus Ponies. This episode did not get made, possibly because it sounds too sad, or because Hasbro wants to keep possibilities open.
The topic would eventually be addressed in Season 4's "Flight to the Finish", though it's ultimately left ambiguous as to whether or not Scootaloo will ever be able to fly.
According to Amy Keating Rogers, "Filli Vanilli" initially started out as "The Return of Flutterguy", but it was changed to "Flutterfear" due to the title being too spoilery. Someone suggested "Filli Vanilli" and she stuck with it.
Pinkie Pie's "Piggy Dance" song from "Baby Cakes" was originally written for "The Best Night Ever" as a longer song to the tune of the "Chicken Dance", but was cut at the last minute due to time restrictions.
The "Smile Song" was originally going to sound very different, and include a talk-sing "patter" section with lines by a number of characters (most of whom ended up either only having silent cameos in the episode or not appearing at all): Derpy Doo (then named as such due to Amy Keating Rogers not having been aware of the full name "Derpy Hooves" at the time), Hairy, Shimmy Shake (who was to be Twist's mom), Rarity, Fluttershy, multiple Polo Ponies, and multiple cows.
Some songs were shortened due to time constraints, although at least two confirmed cases (Love is in Bloom & Find a Way) did get released in full later.