By default, the Prince from the original trilogy is highly skilled with a sword, using it to fight most of his enemies, and also a skilled athlete, able to climb ledges. Unlike his modern iterations, he lacks his wall running abilities. His other abilities in the first trilogy are mainly affected by the potions he drinks and the specific weapons he wields.
Starting from "the Shadow and the Flame", the Prince occasionally loses his weapons, only to recover them (in Prince of Persia 3D) or earn better ones (such as the different swords and the fireball attack in "the Shadow and the Flame").
In the Shadow and the Flame the prince loses his first sword after fighting the skull at the rope bridge inside the cavern, just before he escapes on the magic carpet. His second sword is actually a broken one he finds in the ruined kingdom, notably less effective than his first one. The third sword he wields is his father's when he finds it in the palace's throne room.
The specific powers granted him vary with the potions he drinks, and range from gravity reversion and darkness (the first two games) to feather fall (the entire first trilogy), to invisibility, arrow protection and super jump (Prince of Persia 3D) to name a few.