The majority of approaches at airports, in particular major airports, are called straight in approaches, since it is less risky flying these types of approaches and they work well with the Instrument Landing System.
With this in mind, the absolute minimum for a Boeing 737 is 5-10nm from the touchdown zone. Usually aircraft will be vectored in by ATC from 15-20nm away in a straight line or on base leg, giving the crew time to get the aircraft lined up and prepared for landing.
During a typical ILS approach, the localizer is usually picked up by 10nm and the glideslope usually comes alive by 6nm, though there will be variation from airport to airport. For example, with Atlanta, Georgia, the ILS approach commences at 13.6nm.
Obviously there are exceptions, such as Kai Tek, which was notorious for the bent approach at low altitudes with a Boeing 747. Aircraft didn't have much room to line up with the runway, so it involved a lot of skill and concentration. Norwich airport runway 09 also has a DME arc approach too, which leaves just under 10nm to line up with the runway and follow the glideslope.