I've been sitting crisscrossed (Indian Style) a lot lately, actually. I'm doing it so much that I'm actually rubbing the skin off of the top and outer sides of my feet. Since the cushion of the chair that I'm sitting on while on the computer is made of some sort of vinyl, and I'm usually sitting on my feet--and they're barefoot... yeah, it's not a good mix. I think this issue actually started from when I was playing Mariokart 8 for long periods of time--and the couch in the basement is leather, so same issue there--because I've been sitting crisscrossed for years and haven't had this problem. I also sit this way in the rocking chair a lot, though that is covered in fabric, so my feet don't suffer for that so much. My ankles do, though. Since I'm sitting on them for hours at a time, while bend inward--and since I oftentimes end up falling asleep--they hurt like hell afterward.
Outside of those three places, I don't think there's a particular sitting style I use. I kind of just sit however I'm comfortable with in the moment. Though I have noticed I sit on my left foot a lot. Not sure why.