It depends on the bullet AND the caliber!
The rule of thumb is one bullet diameter of seating dept is normal, and anything less than that may not be enough to hold the bullet tight to resist magazine recoil movement.
For example, in a .30 caliber, 0.15" is half a diameter, or less than 1/6" seating depth. In a .223, .112" or 1/9" is half a diameter.
That 1/8" seating depth might work for a .223 but not for a .358 Winchester.
Generally, the limiting factor is the throat dept on your chamber. I believe SAAMI maximum cartridge dimensions give the minimum seating depth using the longest bullet in that caliber.
The bullet-to-case assembly must be strong enough to resist rough handling and dropping, of course.
HTH
John