In May 2013, I started a thread on the Geek & Sundry forums, called Geek Girls We Love (mainly for fictional characters). Since then, I've occasionally thought about putting the list on my website. In May 2014, I finally did so. (Inspired, I suppose, because of other pages I've recently made for Creepy Kids and Goth Girls; though geeks are generally my favorite kind of girls.) Please note that while it's true for the majority of these girls/women that one of the reasons I like (or love) them (but certainly not the main reason) is that I find them attractive, that's not true of all of them (mainly because a few of them are just too young for that.) But the main reason they're all included here, the reason I like (or love) them all is... you know, because they're geeks. (Some of them are simultaneously very cool; being a geek and being cool-even in a mainstream way-are not mutually exclusive.) But the important thing about all these people is their intelligence. Some of them are geniuses, and some just above average, but they're all smart. (While the original idea was to list geek girls/women, many of the people on the list aren't geeks, but nerds. And some are both.) For many people, this may mean being ostracized to some degree, but not necessarily. For many, it may mean being shy or socially awkward, whether others hold their geekiness against them or not. Some may be sarcastic or snarky, but it's not a requirement. But the main requirement is simply having geeky interests. Most of the people on this list will be adorkable, but there are also many adorkable people I wouldn't call geeks (who therefore aren't on the list).
No doubt I'll add to the list from time to time... But you may also want to check out the thread for suggestions other people have made there, not all of which I'll include here.
Abby Sciuto on NCIS (I've never seen the show, but I've always sort of wanted to, just because of her; she's also on my goth girls list)
Abby Yates, Jillian Holtzmann, Erin Gilbert, and Patty Tolan in Ghostbusters
Aimee Brightower on Galaxy High School (possibly my first animated crush)
Alex Dunphy on Modern Family
Ami Mizuno (Sailor Mercury) on Sailor Moon (my favorite Sailor Scout)
Amy Farrah Fowler on The Big Bang Theory
Andy Jensen on Kyle XY
Annie Mack on The Secret World of Alex Mack
April Nardini on Gilmore Girls
Bernadette Rostenkowski on The Big Bang Theory
Carol Seaver on Growing Pains (one of my earliest live-action crushes)
Chloe O'Brian on 24 (I've never seen the show, but I'd kind of like to, mainly because of her; she's also on my goth girls list)
Chloe Sullivan on Smallville (the best thing about the show)
CIA Scientist Anna
Claudia Donovan on Warehouse 13 (possibly the coolest geek ever)
Dana Scully on The X-Files (more geek-bait than geek, but still she was very smart)
Daria Morgendorffer on Daria (probably the snarkiest person on this list, which is saying a lot)
D.D. Cummings on She Spies
Diane Hughes on Jake 2.0
Edward Wong Hau Pepelu Tivrusky IV on Cowboy Bebop
Ella Lopez on Lucifer
Felicia Day (see favorite actors), in many of her most familiar roles, such as Cyd "Codex" Sherman in The Guild, Dr. Holly Marten in Eureka, Charlie Bradbury in Supernatural... and, of course, herself in real life.
Felicity Smoak on Arrow (the best thing about the show)
Hermione Granger in Harry Potter (though I haven't read the books, and I assume she's more of a nerd there than in the movies)
Irene Quinn on The Tomorrow People
Jemma Simmons (and to a lesser extent Skye) on Agents of S.H.I.E.L.D.
Jordan Cochran in Real Genius (another of my earliest live-action crushes)
Juliet Street on Earth: Final Conflict (more of a punk than a geek, but she was a very smart hacker, so...)
Katie Andrews on No Ordinary Family
Ki Swan (and to a lesser extent Jenny Matrix) on Video Game High School
Lisa Simpson on The Simpsons
Louise Fisher on Inhumans
Marsha Holloway in Zoom: Academy for Superheroes
Phoebe Spengler in Ghostbusters: Afterlife
Saffron Monsoon on Absolutely Fabulous (I'm just mad about Saffron)
Simone Foster, Darlene Merriman, Janice Lazarotto, et al. on Head of the Class (I'm sure there were several other girls on the show, all of whom could be included on this list, because the show was about a high school honors class. But these are the only three I clearly remember, and Simone was always my favorite)
Stella on John Doe
Tina McGee on The Flash
Toshiko Sato on Torchwood
Twilight Sparkle on My Little Pony: Friendship is Magic
Velma Dinkley on Scooby-Doo
Willow Rosenberg on Buffy the Vampire Slayer
Winifred "Fred" Burkle on Angel
Yomiko Readman in Read or Die (my favorite bibliophile ever)
Yuki Nagato on The Melancholy of Haruhi Suzumiya (not sure if an emotionless alien robot technically qualifies as a geek or a nerd, but if she were as human as she looks, she'd definitely be one)
honorable mention:
Some people I considered putting on the list, but wasn't quite sure about include:
Alexis Castle from Castle;
Diane Court from Say Anything...;
Dr. Claire Saunders, Ivy, and Dr. Bennett Halverson from Dollhouse;
Darlene Conner from Roseanne;
Gabrielle from Xena: Warrior Princess (at least for the early part of the series);
Liz Lemon from 30 Rock;
and probably others. (No doubt there are some characters that haven't even occurred to me, but whom I'd definitely put on the main list or at least give honorable mention, if I thought of them. Though there are also some on the G&S thread that were mentioned, whom I considered giving honorable mention, but ultimately didn't even do that much. Which is why I suggest you read that thread.)