he / him
'On accident' is picking up a little bit more popularity, apparently, with the youth of today - specifically within the US. However, 'by accident' is the widely more commonly accepted/used phrase, and to be honest, sounds a little better to these ears.
Call me antiquated, but I'd definitely recoil a bit if I were to hear somebody say 'on accident' in my vicinity. I presume it's a direct mirroring of 'on purpose', but yeah, like @dodoriazarbon, it just doesn't sit particularly well with me.
'By' accident sounds awful to me. *shrugs*