I am a lefty, but with lots of cross-dominance (I think).
I play paino, drums, bass, guitar and a few other instruments. All right handed, if it applies. On drums this crossing has been very beneficial.
I have good spacial awareness, very good hand-eye coordination, and can track moving objects well. I sometimes forget which is left, though.
Left-handed people are different. They just have a slightly different way of approaching the world, IMO. I can't really define this, but I can often tell when a person is LH'ed without seeing them write, or which wrist has a watch on it (almost always the non-dominant hand). I don't know what, but there is something there.
I don't buy that lefties are more intelligent than righties. I've known many less than bright lefties to think that. There are plenty of retarded and autistic LH'ers; more than in the general population, in fact. I belive that whatever events in-utero contribute to hand-dominance, also can cause cognitive deficiencies.
Lefties have a thicker corpus callosum (the band of connective tissue that connects the two hemispheres), which might account for the ability to think both logically/sequentially and creatively/non-sequentially.