In Defense of Sherlock Holmes as an ISTP
Since I think we can all agree that Sherlock is an introvert with a preference for thinking, I will address the two remaining aspects of his psychological type people tend to disagree on: whether he is a sensate or an intuitor, and what the orientation of his traits are. (i.e. J versus P)
On sensing versus intuition, my premises are as follows:
1.) Sensing is generally systematic in approach, where Intuition is nonlinear.
2.) Sensing is deductive in nature, whereas Intuition is inductive in nature.
Even casual fans are familiar with Sherlock's famous quote, "When you have eliminated the impossible, whatever remains, however improbable, must be the truth." This is demonstrative and exemplary of the systematic, step-by-step approach Sherlock took in unraveling the mysteries. In every one of his adventures, Sherlock examined all of the clues and data, eliminated the impossible, and, when necessary, again went out and sought the remaining data he needed to narrow it down to a single possibility. This is deductive reasoning.
In fact, Sherlock went to great extents in actively thwarting inductions and theories, often having conversations on theater, music, and other miscellany with Watson to avoid drawing any inductions prior to accumulating all of the facts. Intuitive thinkers can't help but draw inferences; this is what Intuition does! An excellent example of an INTP sleuth would be L from Death Note. (I must confess, however, that I somewhat disliked the show since L's inferences were far too often based on circumstantial evidence that he had simply used to bolster his internal model.)
On extroverted judging functions (J) versus introverted judging functions (P), my premises are as follows:
1.) Extroverted judgers (Js) are concerned with using their perceptions to arrange the external world of people and things, whereas introverted judgers (Ps) are concerned with using their perceptions to arrange the internal world of thoughts and ideas.
2.) To wit, Ps tend to be "in it for the game" people, whereas Js are generally "in it for the payoffs" people.
Sherlock is, beyond any shadow of a doubt, in his profession for the love of the game. This is evidenced by his impatience and depression when he has no cases to occupy him and to exercise his abilities upon. Further, he has no interest in glory or accolades. Addressing premise number one, he is perfectly content, to come in, do his job, and fade into the background. (After putting on a bit of a show of it, mind you. He was a bit of a show-boater, to be sure.) He never shows any inclination whatsoever to exercise control on the external world in any large way.
(One could make the argument that taking care of Moriarty was, in a way, exercising control on the external world, but I think even more pointedly Moriarty represented the Ultimate Game to Sherlock, and the betterment of London was a side benefit. Also, to get a bit meta, Doyle had originally intended for Sherlock's battle with Moriarty to be the end of him, so he concocted a villain worthy of taking Sherlock's life.)
More circumstantially, Sherlock's proclivity for sensual pleasures such as tobacco and cocaine, not to mention his tolerance for abject slovenliness, further lead me to believe him to be a P. (Keep in mind this was the Victorian era; during the Victorian era, it was perfectly socially acceptable to dope up before breakfast and pimp-slap your hired help for looking at you wrong, but men and women were expected to be chaperoned on dates. Had the times been different, it's not extreme to think Sherlock may have been a bit the Lothario.)
These are the reasons I feel Sherlock is an ISTP. If you're looking for an INTP in the Holmes universe, I would suggest that his older brother Mycroft is an excellent example. Sherlock even goes so far as to say that he suspects Mycroft of being the more intellectually capable of the two, so there you go!
(As for why I, an INTJ, took Mycroft as an avatar despite believing him to be an INTP, I leave to you to speculate upon.)