The 80s saw a major change in how toys could be advertised. A regulation that prevented companies from making cartoons based on a toy line was dropped* by the Reagan administration. This opened the door to several lines, including Transformers, Jem and the Holograms, Captain Power and the Soldiers of the Future, and My Little Pony**. Hasbro created the My Little Pony toy line in 1981, releasing the ponies in 1982, with several cartoons based on the toy ponies. The cartoons were aimed at young girls, the same demographic the toys were. One little girl in particular, Lauren Faust, gave her My Little Ponies distinctive personalities as she played with them.
Ms Faust grew up to be a writer and creator, particularly of cartoons. She worked on such series as The Powerpuff Girls before helming one of the biggest cartoons of the 21st century - My Little Pony: Friendship Is Magic. In creating that cartoon, she took the personalities her toy ponies had and gave it to the Mane 6 - Twilight Sparkle (a book smart but naive unicorn), Rarity (a fashionable but vain unicorn), Fluttershy (a kind but shy pegasus), Rainbow Dash (a brash tompony), Applejack (a down to earth but workaholic earth pony), and Pinkie Pie (a genre savvy party pony).
There are many keys to the success of MLP:FIS. The big one is that it has a broad appeal. While the show is aimed at young girls, who Hasbro wants to pressure parents into buying the toys, there's enough in the series to attract a large peripheral demographic***. Shout outs and homages abound, from Looney Tunes to Benny Hill; something for everypony. In addition, Hasbro itself has not bothered to take down episodes from various sites, including YouTube, in part because company officials have no idea how to react to the show's success. Since the series exists to sell ponies and ponies are selling, the officials have decided to let things stand.
Another key is how the show presents dilemmas for the Mane 6 to solve. In the 80s, typically there was one character who was designated as being always wrong, even if that character's idea made the most sense. In the Dungeons & Dragons cartoon, Eric the Cavalier held that designation - he'd would always make a suggestion that the others would reject for the group's, even if his idea made more sense. In MLP:FIS, no pony has that designation. Conflict can come from any two characters, and the solution is to work together and use each others' strengths without making either pony feel bad, using the power of friendship.
A third reason for the success is the treatment of the fans. Fanon names for minor ponies, such as Derpy Hooves and Doctor Whooves, have become canon. This is unprecidented. Yet, it lets fans feel more included, something that goes with the message of the series. The names don't affect anything with the Mane 6, but some ponies, including Derpy Hooves, have made more appearances as a result. There is a synergy between the creative crew and the fans.
Over and over, the term "respect" has come up in respect to making a successful remake. In this case, the respect isn't necessarily towards the original material. Instead, it's respect towards the fans that has made My Little Pony: Friendship Is Magic a success.****
Next time, an anti-war TV series.
* Although ads for the toys still could not air during the show
** Please hold your squees until after you've read the column. :)
*** The last time I saw such a peripheral demographic was in 1995 with /Sailor Moon/. The general reaction from the older male periphery then was, "What did I watch and why am I still watching?", a reaction seen today with new bronies.
**** You may now squee. :)