While there are certainly women in the world who read comics, the vast majority of comic readers are male. Most comics feature superheroes, and superheroes are mostly adolescent male power fantasies.
Wimpy Clark Kent is actually the insanely powerful Superman!
Nerdy Peter Parker is actually the web-slinging Spider Man!
Sickly Bruce Banner, when he gets angry, turns into the impossibly strong Incredible Hulk!
and so on.
Most female characters in comics play into those adolescent fantasies- Mary Jane Parker is Peter Parker's insanely hot girlfriend for example. You don't have alot of "scrawny Sally Samuels is secretly Mighty Lass!" So, between all of the images of male power, and women as eye-candy, traditional comics didn't really offer a whole lot for the average female reader.
Notice I said "traditional comics." In recent years (the last 2 decades or so) more and more comics have been released that have appeal beyond the traditional base of teen boys. So, if you are a dude who loves comics, and you have a girlfriend/fiance/wife who you would like to get into comics as well, here are some titles I would recommend:
Fables is a series from DC's Vertigo imprint by Bill Willingham. It doesn't feature any superheroes, so if your SO (significant other) is averse to capes, this is a great place to start. The story features characters from fairy tales who secretly live on a block in New York City. So, there's a reference point there- everyone knows Big Bad Wolf, Snow White, Beauty and the Beast, etc. The story kind of turns all of those characters on their heads by putting them into a modern, real world setting, and features a plot that starts out as a murder mystery, but gets increasingly more complex, and epic as it goes along. Tell your SO it features Cinderella as a badass spy if the previous description isn't enough to entice her.
Anything by Gail Simone
If your SO isn't averse to capes, try handing her Birds of Prey, Secret Six, Wonder Woman, or anything else by Gail Simone. Gail Simone is a great comic book writer who happens to be a lady. She first came to prominence through her website "Women in Refrigerators" which directly took on the way superhero comics tend to portray women as weak, and as victims. Every book she writes features incredibly strong female characters who kick just as much butt as their male compatriots, but who also have human flaws and frailties. On top of that, her comics tend to read like the funniest, darkest, goriest Quentin Tarantino movie that you've ever seen.
Anything by Joss Whedon:
If you have a geek girl SO, there's a very real chance that she loves Buffy the Vampire Slayer, Angel, Firefly, and Dollhouse, all of which are, of course, creations of one Mr. Joss Whedon. Oh, and Dr. Horrible's Sing-Along Blog too. Anyway, Joss Whedon is probably the most prominent creator of TV shows that girl geeks love. But did you know he sometimes writes comics? It's true! He wrote, amongst other things, a pretty stellar run on Astonishing X-Men. Hand your SO the Astonishing X-Men graphic novel "Gifted," and when she says "I don't really care for the X-Men" tell her, "But Joss Whedon wrote it" and she will finish it within a day.
Neil Gaiman's Sandman:
Another one for the non-cape loving set. Sandman is one of the great works of comics literature, and it's also beloved by goths, and lady nerds the world over. Sandman is the story of Dream, who is one of the Endless- a family of living concepts- and deals with the subject of dreams, and storytelling in general.
Look, the truth of the matter is, there aren't girl comics, or guy comics. There are just comics. Comics are a storytelling medium. As I said earlier, they were traditionally written in a way that was kind of off-putting to your average geek girl, but really, chances are, if you hand your SO something that's really good, she'll enjoy it. So give her Invincible, Watchmen, Invincible Iron Man, Iron Fist, or whatever else you really love. Chances are, she'll really enjoy it.