Morpheus has got to be one of the coolest mentors out there. He definitely gets major points for style alone. Aside from that he is a well respected leader in the "real world" of Zion, and is convinced that Neo is The One who will save mankind from the machines.

To do so, Morpheus must use his cool factor to convince Neo to free his mind and trust in him completely. It's a pretty big task but somehow he manages to pull it off without breaking a sweat.

Top quote:

Morpheus:  "I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it."