In this day and age, an address on a resume is not always necessary. While the employer could send an offer or rejection letter by snail mail, most likely they’ll opt to shoot you an email.
However, some employers may only want to hire local candidates, perhaps due to local tax incentives or for viability. Adding an address to a resume may be required for those positions, but it could also exclude you from the candidate pool if you’re not within their boundary parameters. Some also pay attention to where you live because they want to know how much time you'll need to commute and if you're a tardy risk.
On the flip side, for those employers who only want local candidates, leaving your address off of your resume may give you a fighting chance. You could get called in for an interview so they can see if they like you, and then your distance will matter much less to them.