Well I'm left handed, and it's been my experience that it's rare (but not impossible) for lefties to have 'nice' handwriting. I read something a long time ago about this; since lefties drag their hand across what they just wrote, everything gets put out of alignment since you can't see what you just wrote, or something like that. My handwriting isn't horrible, but it's certainly not as neat as right handers. Looking at the people that I know, left handers always have worse handwriting that right handers.
Yep. Another southpaw here, and without lined paper everything I write slopes downward towards the right as I can't see what I've already written. Still, it's better for me than for my parents' generation, when left-handed children were forced to become right-handed. I'm convinced my aunt was born left-handed because she's always had poor hand-eye coordination and her handwriting is atrocious.