I cast right and reel left. I am right hand dominant. I write with my right, golf, hockey, everything. When I took up fishing as a kid, I can't remember how I did it. I know that I cast with my right, that's a no brainer, but I couldn't remember what I did reel wise. I thought that it was with my left, but when I took it up again recently, it felt odd at first. About half an hour of chucking a rapala and it felt normal. I've only reeled with my left in fly fishing. I wouldn't even consider reeling with my right, as I would feel like I'm all thumbs trying to control the rod with my weaker, left arm. I have better line control with my left hand than I do my right also.
Cast right, reel left is 100% natural to me.