The Spokesperson for Religion
This is the person who has just found God, Allah, Buddha, Krishna, or some magical turd in the Atlantic, and must tell you about it. Right this instant. He will walk up and down the train screaming at you about how you will be damned if you don't follow his god. If you ignore him (stare past him, read a book, etc) he will frantically wave and flail IN YOUR FACE for three minutes until he realizes you will slog him in the throat if he keeps it up.
Your New Best Friend
This is the person who resembles you in no way; typically he or she will be on the opposite end of the age spectrum. But you do, read, or wear something that s/he just had to come talk to you about, because it's the greatest/coolest/most interesting thing ever. Some will be polite and after a brief inquiry let you go back to living your life; these people are okay. Polite social behavior is fine. Unfortunately, this is the subway. More often than not, the person will use that topic to segue into how you are now great pals because you have XYZ in common. He will inquire about your life, your other hobbies, and a plethora of details you don't care to tell him. For these people I make up lies, since I don't trust any batshit crazy subway riders.