Which pony is known as the 'Great and Powerful'?

The pony known as the “Great and Powerful” is Trixie.

Trixie is a blue unicorn magician who travels around Equestria performing theatrical magic shows. She refers to herself in the third person and uses the grand stage name “The Great and Powerful Trixie,” making the clue a direct match rather than a judgment about her actual magical ability.

She first appears in “Boast Busters,” the sixth episode of season 1, which originally aired on November 19, 2010. In Ponyville, Trixie boasts that she defeated an Ursa Major, but her story is heavily exaggerated. When an Ursa Minor later threatens the town, Twilight Sparkle—not Trixie—calms it.

A common mix-up is confusing Trixie’s boastful title with a formal rank or royal title. It is her self-styled performer name. Over time, Trixie changes from a rival and antagonist into an ally and friend of Starlight Glimmer.