A Horcrux is a soul container for a fragment of the creator's soul. The creation of the container requires the splitting of the soul, but whether each ritual halves the soul every time or the split is carried out evenly is never determined. In any case, <PERSON> is running around with at most one-eighth of his soul for much of the series.
Presumably a diminished soul does affect one's mental capability, given the many warnings of the dangers of creating a horcrux. We know <PERSON> (who invented the first horcrux) did not create multiple horcruxes, because <PERSON> shocked Professor <PERSON> when he asked about the best number in which to split his soul, taking number seven to be correct from the conversation.
He does have seven soul fragments in existence at all times, despite not realising that <PERSON> is one of his horcruxes. Initially, he has the Diary, the Ring, the Locket, the Cup, the Diadem, <PERSON>, and himself. 773
Once the Diary is destroyed, he makes <PERSON> into his final horcrux (believing he needs one more for seven), giving him the Ring, the Locket, the Cup, the Diadem, <PERSON>, <PERSON>, and himself.
So what are the dangers of having one or more horcruxes?
Does having so little of his soul remaining affect <PERSON>? It's hard to say, but it can be argued that he was more of a sociopath in his teens at Hogwarts and slowly devolved into a complete psychopath in later days. Whether this can be attributed to the effects of continually dividing his soul, to other rituals he undoubtedly performed, to gradual mental impairment as an evil overlord, or to sheer mental breakdown from living as a possessing spirit for over a decade is impossible to determine.
A lot of <PERSON>'s arguments turn out to be incorrect. He claims <PERSON>'s soul was so unstable it broke apart when he attacked Godric's Hollow. We know this to be untrue (though <PERSON> may have believed it to be true when he said it) because <PERSON> is still around, and he later splits his remaining soul to create the Nagini horcrux.
The whole <PERSON> argument is also questionable because we never see it realised in any way. In any case, asking a psychopath to be remorseful is quite impossible, and if turning into a psychopath is the effect of one or multiple horcruxes, then it is a fallacious argument.
Are the dangers of horcruxes real? Or are they exaggerated by a Ministry unwilling to see the rise of more invulnerable Dark Lords? Only <PERSON> really knows. 773