Reid- INTP. All of his rants about facts and theories are super Ti-Ne. He suppresses his feelings and has trouble in social situations which strikes me as inferior Fe.
Gideon- INFJ. He has some penetrating Ni that allows him to notice patterns in cases. His Fe is subtle but he gets emotionally involved in cases and is good at reading people and appealing to their emotions.
Elle- ESTJ. She had that Te toughness and I didn't pick up on too much Si but I got some from her like how her dad was in law-enforcement and she followed in his footsteps, etc.
Hotch- ISTJ. His Te is pretty clear, he likes to be in charge, goes off of facts, etc. But he's too withdrawn to be an EXTJ and he has no real Ni. I see more Si like his loyalty to the team and his want for family, etc.
Prentiss- ESFJ. I would say her Fe is very clear. She cares about everyone on the team pretty quickly, wants to be liked, and is sometimes too prying. I don't get all that much Si from her but I don't get any Ni either. She could possibly be an ENFJ but seems more ESFJ.
Rossi- ENTJ? I would say that fits. He gets attached to only cases he personally relates to and even then, very rarely. He has the Te-Ni particular-ness and he's good at being in charge. He also has the pattern-noticing skill that often comes with Ni.
JJ- ESFJ. She likes a bit of gossip (shown in that episode where Garcia is sleeping with a co-worker) and she is very good with people. She also has pretty distinct memories of her small town, etc.
Morgan- ESFP. I definitely thought ESTP at first but that was more based on stereotypes. He clearly uses Se (good in the moment, knows his surroundings) but I think he uses more Fi-Te than Ti-Fe. He relies more on facts and results than logic and curiosity and he's actually quite feeler-y. He's got Fi-style loyalty and compassion for people like Garcia and his mom. He also has a certain self-awareness and distinct sense of self.
Garcia- ENFP. She could be an INFP, technically but she seems to have more Ne than Fi. She likes a variety of things, all of which stimulate imagination (graphic novels, online role-playing games, etc.) and she has a need for individuality (Fi) which is expressed through how she dresses, and decorates her workspace and apartment.