I wouldn't say MLP is the best show in existence, but I would say it's certainly a worthy show to be watched and one of the best out there.
Per why I watch it: one of the primary reasons has been with the writing being actually gender neutral on my ears. Despite the name and franchise history the new Friendship is Magic was written in a way to appeal to male and female audiences and older and younger audiences alike. I'd venture to say that enjoying MLP - or any cartoon today - is like an adult liking a Dreamworks animation like Wall-E or Wreck it Ralph.
In this comparison, both examples (MLP, Adventure Time and Wall-E and Wreck it Ralph) are shows that are primarily marketed towards children and younger viewers. Yet they do have that older generation viewer base. How does this happen? I would put it into the writing. Adults can grasp more complex themes than children and young people and when a show's writers drop complex themes and or references to ideas that the intended may not get, the adults may get it. And doing so serves to attract and amuse older audiences.
Beyond this, one of the primary standing reasons I've found for people to like MLP is in its animation quality and accessibility of the art work and style. The characters match well with their environment and are not offensively loud or grotesque to look at. And at times, they can be intimidating in their own right. In MLP's case, more-so when compared to the general environment, at least.
Psychologically I've found many bronies can relate to the characters of MLP fairly easy which helps for audience appreciation. And every once a while the show will touch up on socially important issues that help to relate to most of the viewer base. Most recent with bullying with the episode Bad Seed.
And let's face it, we're all nerds here people. And even if we're done with that stage of life or already know how to deal with it, it only helps the case if we can relate more to the show via situation experience.
There was also a study I read examining the brony phenomenon as conducted by a professor of behavior studies at the University of Boston that concluded the prominence of MLP is a side-effect of events within our lives. The most prominent viewer groups are those in college or the later half of HighSchool leading to the conclusion that in some shape or form the events of 9/11, two major wars, and the continued stressed environment of the economy and the Horseman of War rearing his head in the Middle East are factors that make the relatively peaceful, and easily relatable world of MLP attractive.
It could go up to debate and the man's study is ongoing. But it's a certainly better explanation that what I've heard prior which is heavily reliant on Freudian sciences and probably based primarily on people who have malignant psychological issues and who make up a minority of the fandom. And is easy to sell to Fox and other media outlets.
Beyond this and returning to the appeal of the show at large: it's got an immense world behind it with the surprising advantage of it being primarily unexplored which allows for fan exploration. Fan art and Fanfics add to the community and the world in surprising ways and allow for a creative freedom the creators of the show do not mind, or straight up appreciate.
The fanculture itself is also very... colorful to say the least and I can find it amusing and astounding. It produces some master works of fiction, art, and music which blows me away. The quality is also matched by the rate at which it can come out.
Within the day of the airing "Bad Seed" its keystone song "Babs Seed" was remixed and covered at least a dozen times. And then it continued to explode being probably one of the most remixed and fan covered songs since "Love is in Bloom" and "Winter Wrapup".
It's also a point that when they do it, the songs (even the background music) is well written and composed element of the show.