The way I always justified the usage of the axiom of choice to myself (which I haven't had to do very often) is as an expositional convenience. If somebody told me that I couldn't use the axiom of choice anymore, I would take all the theorems I know about commutative rings and replace "Let R be a commutative ring" with "Let R be a commutative ring with a maximal ideal", and then I would go about my business, since nobody cares about the crappy ring you slapped together which doesn't have a maximal ideal.