Huayna Picchu
The most popular hike
Huayna Picchu (aka Waynapicchu) is the peak that is behind the llaqta in almost every photo of the ruins. This is by far the most popular hike, has the fewest people allowed per day and is the narrowest with the most exposure. It is now route 3A.
Do not do this hike if you are afraid of heights or suffer from vertigo.
Huayna Picchu is partly popular because of the view back down onto the llaqta, but also because it has a cave around the back side with a moon temple in it. The peak itself is also covered with walls, steps and other ruins.