That being said, here are three female characters on TV who I not only like, but I really identify with.
1. Liz Lemon from 30 Rock
While she got rather less smart as the show went on, I still absolutely connected with her. She was socially awkward and, often, socially apathetic, and while she occasionally tried to change who she was and embrace more traditional social norms, most of the time she just found acceptance in the fact that she was always going to choose food over human interaction. She also had very low tolerance for stupidity in the world around her, had a tendency toward elite snobbery, she vastly preferred the known and the routine to adventures, and, while she was generally a smart and competent human being, when she goofed up, she goofed up a lot.
I connect with all of those traits. When I first watched 30 Rock, I completely connected to Liz's social awkwardness. I loved that she was allowed to be both just a normally awkward person. This wasn't some kind of "idiot savant"-style character, a Sheldon Cooper or whatsherface from Bones, who are geniuses in their careers but truly incompetent everywhere else. Liz was smart, capable, fairly awkward, and often oblivious. She was like an actual person.
2. Willow Rosenberg from Buffy the Vampire Slayer
God bless Joss Whedon for writing interesting nerd girls, starting with Willow. She was tied with the snarky vampire Spike for my favorite character throughout the show.
Once again, it's a great blend of smart and socially odd. Willow was extremely intelligent and settled easily into her vampire-fighting group role as a researcher. Eventually she discovered she loved the challenge and intricacies of magic, and she quickly became very adept at it.
At the same time that she was extremely confident in her intellectual abilities, she was often hesitant or uncertain when faced with social situations she couldn't predict or control. She was a faithful friend, a quiet voice of reason, the one who spoke up against her friends' more emotionally-charged decisions, but worked to support them whatever they chose.
Especially in the first couple seasons, before Willow really finds settles into adulthood, I see myself very strongly in the character. She's a quiet nerd girl, the one who would be most likely to sit in the back of the room and then, out of nowhere, offer a comment she's been pondering for awhile (which prompts someone else to say, "Oh! I didn't even know you were here").
3. Daria Morgendorffer from Daria
I actually started watching Daria because my good friend Sarah said I reminded her of the title character. We watched the first episode together, and there were three separate instances where Daria spoke out loud almost the exact snarky thought in my brain. I watched the entire series shortly after, and got extremely sad for awhile when it was over, because I knew I'd never find another show that understood me so perfectly.
I love Daria. I love her. She is easily my favorite TV character of all time. She is smart, but bored out of her mind. She's tired of the shallow, superficial world of high school and longs to be somewhere where she can stretch her intellectual muscles, but at the same time she's worried that maybe she isn't as deep or as smart as she appears in contrast to others at Lawndale High. She spends most of her time with her one friend making snarky comments about the people around her, but she's open to being pleasantly surprised by unexpected depths (though that doesn't happen very often).
Daria is in nearly every way a slightly bolder, slightly more cynical version of me. If you want to know how I think about things, watching Daria will give you a really good idea. She's got far more levels than a lot of sitcom characters and she's beautifully consistent with them. The more I watch it, the more I'm impressed with her as a character.
Honorable mentions: Annie from Community, Fred from Angel, Tessa from Suburgatory (season 1, before she also got stupid). Though really, just about any nerd girl is going to connect with me at least a little bit. Uh, but nobody from The Big Bang Theory. I am far from being an Amy Farrah Fowler, thank you very much.
We'll talk about movie characters some other time, but for now: What TV characters do you identify with? Or, if you're prefer, are there any characters that remind you of me? I'm always on the lookout for new shows with new female characters to root for.