I usually see people discussing whether Reid is INTP or INTJ, but I'm not sure either is the case. In fact, Reid strikes me as the "purest" member of the BAU, still a child who is curious about the world, even if he knows more things about it than almost everyone else. It's true that the T trait is more closely related to intelligence (statistically, Rationals are the most intelligent group, Idealists on second place), but not at all as close as it would often seem.
I'm an INxP myself, leaning slightly towards T, and maybe my own type influences my judgment. But growing up, I was the Reid of every school I attended; even teachers would ask me if there was something in the books that they didn't know or understand, but other students didn't quite like me or "get" me, and they still don't. Intelligence-wise, I'd never put myself on the same level as him, he's between 40 and 50 IQ points ahead of me, but I relate to his personality and role in a group. It's a thing that often comes with an intellect that differs significantly from the norm, both afflicting those with higher and lower intelligence. Although my IQ is merely about 140, it makes it difficult to have a natural conversation with others - when using words like "archaic" in everyday chatting and constantly acquiring new information through the other party's words and immediately integrating it into the foundation of all your reasoning skills is perfectly normal to you, others are bound to lose track on your associations and what the hell you're actually saying, creating three options:
1) Keep being incomprehensible and leave people wondering about what you mean, which would be seen as arrogant,
2) Attempt to dumb down pretty much all of your points, which could result in the other person thinking you're underestimating them, and
3) Talk less and observe more, being even more of a know-it-all than you were in the first place and putting yourself even further away from the viewpoint of others.
A person of above-average intelligence, like Reid, has to "morph" between these strategies all the time. Thus, the distance he seems to be keeping from the others might not be a product of a Thinking personality, but a result of being intellectually separated from the rest of the world.
That said, although all team members are excellent at pointing out what kind of person a culprit would be, Reid seems to me better at actually understanding them. Instead of seeing them of problems to be overcome, he is quite good at putting himself in their place. Reid is the only one of the profilers who puts his gun down and takes off his bullet-proof vest to gain an unsub's trust, risking his life to understand and be understood, as shown in "Derailed", "The Fisher King: Part II" and "An Elephant's Memory". Reid doesn't believe in control at all costs, he believes in emotional connections and empathy, and, more often than not, he knows exactly how to disarm a person on the verge of madness, simply by feeling how they must feel.
Some examples of Reid's tendency to relate rather than disconnect:
In the episode "Sex, Birth, Death", he says "I know what it's like to be afraid of your own mind"; while Morgan sees the person in question as a weirdo and a potential future danger, Reid sees him as a person, trying to see the world from his perspective, even using his own emotions to understand him. In "Derailed", he plays along with a psychotic man's fantasies by relating to his feelings and stop trying to reason with his subdued sense of logic, and in "Somebody's Watching", he quickly finds the exact words that will make the stalker lose her temper and self-control, making her easier to take down. At that particular moment, he was cornered and emotionally distressed himself, but he was still able to connect with the unsub, suggesting that he does it more or less automatically and that striving to understand and identify with others comes naturally to him. He is kidnapped by a man with split personalities in season 2, and while two of the personalities have treated him harshly, he looks genuinely sorry when the man is shot and dies while in his kinder personality - while an event like that would undoubtedly have a tremendous impact on a Thinker as well, Reid shows empathy even towards a man who has beaten and tortured him, almost killing him at least once. I, as a person between T and F, would definitely not empathize in such a moment; maybe later, but not then and there. I think that this shows a tender nature that few Thinkers have.
Many would attribute his ability to put himself in someone else's shoes to his intelligence, but I think there's something more to him. The actor who plays him has confirmed that he has Asperger's Syndrome, a diagnose thought to be related to the INTJ, INTP and ISTJ types - I agree that he has it, but I'm an Aspie too, and that doesn't make me robotic or emotionless. And while we're at it: If Reid's intelligence had only been slightly above average, would we even consider the possibility of him being a Thinker, or would his empathy be so obvious that we couldn't have questioned this particular preference?
All in all, I have a hunch that Reid might actually be a Feeler: An INFP, to be precise. While INTPs will often seem arrogant without that being the intention and INTJs can sometimes actually be arrogant, INFPs usually come across as merely oblivious, which, in my opinion, also applies to Reid. And honestly - what kind of T, including myself, who is almost not a T at all, would abandon all logic to connect with a man who had lost all his sense of reason? Definitely not an INTJ, and probably not an INTP either.
I bet I'm gonna get a whole lot of protests for suggesting a different personality type for him, but I really believe he's a Feeler, so I don't think any angry comments will make me change my opinion Still, feel free to disagree as loudly as you wish, rational arguments can always make me see the light