Now I absolutely must chime in with a rousing cheer for the women of Star Trek: Deep Space Nine.
Kira Nerys and Jadzia Dax, shown here in Season 1 telling Quark to stop messing around and cooperate, which he does, because they're awesome and terrifying.
Jadzia Dax
Jadzia Dax is Deep Space Nine's ultimate renaissance woman. As a joined Trill, she adds her symbiont's centuries of experience to her host's youth and brilliance, eventually finding her place as the fun-loving warrior scientist who (almost) always gets the last word.
She's flying the Defiant in battle. While the Bridge is on fire. Yeah, that's badass.
Why I Love Her: She's pretty much relentlessly awesome. She's loyal, brilliant and brave, like most Star Trek characters, but she's also fun, and she seems to love and appreciate life every step of the way. Growing up, she was my idol for personal, professional and sexual empowerment.
Here, Jadzia faces the blade of a legendary Klingon warrior to earn the right to join a quest of vengeance. When you're a skinny young Trill and have Kor, Kang and Koloth taking you into battle as their equal, you're awesome.
Why I'd Take Her Into A Fight: In hand-to-hand combat, she can take out a Klingon twice her size. As a strategist and a pilot, well, she once defeated a squadron of Jem'Hadar when she was an inch tall in a runabout the size of a coffee cup (it's Star Trek; these things happen). Chief among her scientific greatest hits: the time she discovered the wormhole to the Gamma Quadrant, which necessitated the existence of the whole show. Her worldly experience gives her both encyclopedic knowledge and a deep understanding of people - if you bring her to a fight, she may charm her way to victory without firing a shot.
Bedecked in questionable 21st century fashion, Jadzia goads the conservative head of a news network into ruining his career to make history.
Kira Nerys
Kira is a survivor. From a childhood in a refugee camp, she started fighting for the liberation of her people as soon as she was old enough to pick up a phaser. She grows from the angry young woman from the trenches into a powerful, passionate and wise leader who ultimately faces down her demons to save the galaxy.
This is any one of three thousand times Kira kicks ass and takes names. She does this three times before breakfast.
Why I Love Her: I love Kira for her resilience. She struggles with the Cardassians, with her own people, with her conscience and with the rapidly changing world around her, and she never stops fighting for what she believes in. She makes mistakes. In spite of herself, she can be vulnerable and compassionate and even, sometimes, capable of forgiveness. She's devoted to her people and her culture. My favorite part of her character is her spirituality - her devotion to her faith never wavers, and I love watching how it weaves in and out of the rest of her life.
It should be noted that Kira lays this Klingon flat out after he stabs her in the spleen.
Why I'd Take Her Into A Fight: ALL OF THE ABOVE. The very first time we meet her, she wins a standoff with the Cardassians on nothing but blind hatred; in season 7, she basically leads the entire Cardassian rebellion against the Dominion (which is, I have to say, pretty much my favorite come-full-circle character arc in the history of TV). She's resourceful, capable, and does not quit. Ever. Whatever war you find yourself in, you don't want to end up on the opposite side.
Kira faces down a Romulan fleet with a dead man's gambit for the safety of Bajor. She wins, of course, and schools a Federation admiral in the process. CASE CLOSED.