Wash: I don't know, but if she doesn't give more power to offset the burn through this landing is going to get very interesting.
Mal: Define interesting.
Wash: "Oh God, Oh God we're all going to die"?
Mal: [Talking into the intercom.] This the captain speaking. We might experience some turbulence, then explode.
Wash: I am a leaf on the wind, watch how I soar.
Inara Serra: Mal, what are you doing here?
Mal: You invited me.
Inara Serra: I never thought for a second you'd be stupid enough to come!
Mal: Well that makes you a tease.
The Operative: Do you know what your sin is Mal?
Mal: Ah hell, I'm a fan of all seven. But right now, I'm gonna have to go with wrath.
Jayne: We're going to explode? I don't wanna explode.
Jayne: She is starting to damage my calm.
Mr. Universe: Guy killed me with a sword, Mal. How weird is that?
Mal: You know what the first thing of flying is, Little Albatross? Well of course you do. You can read my mind.
River: I want to hear you say it.
Mal: Love. You can learn all the math in the 'verse, but you take a boat in the air you don't love, she'll shake you off just as sure as the turning of worlds. Love keeps her in the air when she oughta fall down, tells you she's hurting 'fore she keens. Makes her a home.
River: The storm's getting worse.
Mal: We'll come out of it soon enough.
Jayne Cobb: Shiny. Let's be bad guys.
Shepherd Book: I don't care what you believe in, just believe in it.
Mal: I don't murder children.
The Operative: I do.
Answer: She has several mental disorders, presumably she finds shoes confining or uncomfortable. It's notable that when she does have footwear it's almost always heavy calf high boots, instead of slippers or more comfortable shoes.
Grumpy Scot
To add; She likes to dance, and being barefoot it's easier to move around.
lionhead
Something I always wondered is when she goes on the heist barefoot at the beginning of the film, none of the other characters seem to notice or care that she's in bare feet. Even her brother, Simon, didn't try to get her to wear shoes.