You are my hero for writing this, seriously. I wonder, sometimes, how often other people find fictional characters to relate to. Do they just take it for granted? Is that why nobody talks about it?

You don't happen to know what your personality types is, do you? It's just my normal way of quantifying these kinds of things. I'm an INTP.

It might be hard to believe, but I was seventeen and it was the first time I ever came across a character that thought like I did. (In hindsight, that explains why this is the only male character I clicked with SO HARD.)
This was my exact experience. Well, I was in college, but House was the first character ever where I was like, woah, wait, is this what it's like to actually identify with a character? It didn't matter that he was male, that he was so broken down, that outwardly he seems very different from me (I tried to tell people I identified with him, and they didn't believe me). What did matter is that I instantly and instinctively understood him. His motivations and actions just made sense and were true in a way I had never seen on screen before. And it was frequently hard to watch the show with other people in the room--I just felt naked.

I feel personally insulted by the way his character got mangled in later seasons.
A-fucking-men. He was ruined. Not by doing bad things--I could always accept the bad things--but by not being himself. I don't even recognize him anymore. I've stopped watching. And I am heartbroken. One show on TV that understood me, and they couldn't respect the integrity of their main character.

Temperance Brennan Bones . . . Erica Hahn Grey’s Anatomy . . . Sumire Iwaya Tramps Like Us/Kimi wa Pet
Never watched Bones, dropped Grey's before Erica showed up, never even heard of that last one, but I may very well have to seek all these characters out.

she was a journalist, so her "area" was in language rather than science/math. (I love science and all, but it gets old seeing smart=SCIENCE/MATH WHIZ.)
THIS. Far too often the character I'm most able to identify with is the generic science/math dork (or the villain; I won't even go into how much that annoys me). I've got a science/math personality. I studied English. This is not a contradiction.

Amy Pond Doctor Who
I adore Amy, but the Who character I really identify with is River. I feel like she's a personal gift from Steven Moffat to me. She may be more outgoing than I am and infinitely, infinitely more awesome, but she's also a woman who's intellectually driven and technically adept and utterly un-clingy and fucking self-reliant and her first response to stress is to push her feelings down and plow ahead and she makes a horrible first impression and she's secretive and people think she is an arrogant know-it-all and she snarks like it's her job and all those other things I get, but . . . BUT she can also be sexual and caring and maternal and trusting and unapologetically A WOMAN. People like me in fiction ARE NOT WOMEN. This starts to hurt after awhile. River is a goddamn miracle.

Cristina goes to Meredith, then starts SOBBING UNCONTROLLABLY, freaking Meredith out. And it's not over her love life, but that she's frustrated that her education is being stunted. NGL, I teared up. I get that, way too much.
I need to see this. Like, now. Christina (like Scully on the X-Files, and Martha, and Data and Spock) is one of those characters who I see as "on my team" if not fully like me. That scene sounds amazing.

Seriously, thank you so much for writing this. I feel better now.