Okay here it goes!
Neo - ISFJ
Aspires to be the savior of mankind.
Morpheus - INFJ
He has a such a strong vision (that Neo is the One) and ceaselessly tries to make this happen. Also a natural leader.
Trinity - INFP
She believes in Neo even when others don't. Is in a supportive role.
Agent Smith - ISTJ
Ruthless, exceptionally competent, strives to maintain a functioning matrix system. The epitome of group mentality. He likes to work with other ISTJ agents, and wants the whole world to conform to him (literally).
Oracle - ENFJ
Prophet. Loves and appreciates all people. Tends to catalyze change within others, rather than forcing change upon them.
Architect - xNTJ
The logical, emotionless mastermind. Brilliant, but dumb when it comes to understanding human emotions.