For detailed information about the series, see the Friendship is Magic Wiki
Summary of the Verse
The franchise My Little Pony is split up into 4 Generations, with the most popular and most powerful being that of Generation 4, Friendship is Magic. The show follows Twilight Sparkle on her journey to discover the magic of friendship and make friends with 5 other ponies: Rainbow Dash, Applejack, Fluttershy, Rarity and Pinkie Pie. They have battled many enemies along the way, such as Night Mare Moon, Discord, Queen Chrysalis, King Sombra and Lord Tirek, and have used the legendary Elements of Harmony and newly discovered Rainbow Power to defeat them. The show is highly popular nowadays due to its large male following in addition to female, and has become one of the most popular cartoons airing today.
Power of this Verse
The verse's characters start out at roughly Building Level with fodder, before kicking it up to at least Multi-City Block level with some of the lower tiers such as Spike the Dragon. Island level characters come next, with the likes of the Mane 6, Trixie Lulamoon, Shining Armor, Queen Chrysalis and Adult Spike. Rainbow Dash's Sonic Rainboom also shows considerable destructive feats, but we are not sure of the specifics.
After that we have a gigantic power leap with the likes of the Alicorns (and Trixie with the Alicorn Amulet), who are able to easily lift and move both the Sun and the Moon, showing solid Star level power. These characters are contested by Starlight Glimmer, Starswirl the Bearded, The Dazzlings and Queen Chrysalis with a plethora of love absorbed, who have shown power superior to that of 1 Alicorn. Discord and King Sombra is next, who are able to easily match 2 Alicorns at once and win with ease, showing Large Star level via scaling. Discord in particular can move the sun and moon at ludicrous speeds and is an impressive reality warper. However, even they are taken down by the Elements of Harmony, which are shown to be able to defeat all of the villains seen above with ease, proving them to have power far greater than these villains, or at least neutralizing "evil" characters. The Crystal Heart is another powerful artifact that is on roughly even terms with the Elements, if not even farther above. Flurry Heart when her power fluctuated was able to destroy the Crystal Heart.
Lord Tirek, who gains the power of all 4 Alicorns, every other pony in Equestria, and even Discord, is the strongest big bad in the series, reaching well into the Solar System level range when at full power. Above him is Rainbow Power, which was able to easily defeat Tirek, and is the strongest power in the show currently.
Beyond its strength, My Little Pony is also relatively decent in the speed department. Most relevant characters scale up to Rainbow Dash or the Alicorns, giving them solid Relativistic speed (40% SoL). This verse is shockingly powerful compared to what many would think it is as a "little girls show". Don't underestimate them just because they're ponies.
As for Equesteria Girls series, it's a very weak verse with only a handful of powerful characters. Most characters are Human Level as it's suppose to reflect real life logic. With Sunset Shimmer bringing in magic from the Pony World, the verse is somewhat getting more powerful. Many characters like Sunset Shimmer and most villains are at least Town Level tier.
Supporters/Opponents of the Series
Azathoth the Abyssal Idiot
Great and Lovable Peridot
Starswirl the Bearded
Equesteria Girls characters
However, if events involving actual characters from a story or arc in the comics are directly referenced as having happened in the show, then that particular part is clearly canon.