The barber has a split personality and therefore shaves himself - but it's not really "himself". :)

barber either is a chick, a Native American, or wears a full beard which he trims, not shaves.

He can shave himself every other day.

I have spoken.

How about thinking outside the box? The barber goes to the next town over to get a shave. End of problem.

The barber is barbara streisand???

maybe the barber is only 12 and doesnt yet have to shave?

How about another barber? The other barber can shave all those who do not shave themselves, which would include our original barber.

he would not have much business now would he.
if barber A shaves all those that don't shave, that means he has 100% of the market including barber B

If barber B shaves barber A, then that would mean Barber A does not shave 100% of those who do not shave themself, and also that barber B only shaves one person ...and would be out of business in no time

Maybe barber B lives one town over...

i doubt that works when solving riddles

I was thinking the same thing - there are two barbers and each would shave the other. That would fit perfectly with the riddle.

I suspect there is more to the riddle which is missing. The reason being, the riddle as it is written in the post does in fact have multiple possible answers. Usually a riddle is supposed to only have one answer. No? The fact that three reasonable as well as possible answers come to mind and which are:

- the barber has no hair and thus does not need to shave;

- the barber has hair but does not shave or have shaved the hair;

- the barber shaves, as the "all those" encompasses all or everyone. the and thereafter merely adds another set which is meaninless;

suggests that there are one or more constraints missing from the riddle.