When I was in marathon shape last September, I did ~34 miles on a tough section of the Superior hiking trail over the course of 12 hours; base weight was around 8 lbs with full rain gear. All total was a 61.5 mile weekend, hiking was 30 minutes Friday night, 12 hours Saturday and about 9 hours Sunday. Finished a marathon two weeks after that weekend.
With a little better hydration management on my part, I could have easily done another 30+ mile day.
Trip report: http://crazyrunnerguy.blogspot.com/2008/09/blitz-successful-612-miles-completed.html
Other than just walking with a pack on, I believe long, slow distance running is the best exercise for backpacking. It is not incredibly difficult, but those who cover the most distance are those that are the most consistent with their pace. It will also teach you to eat and drink while moving and will teach you to monitor your body's physical systems. It will also teach you to manage your thoughts and control your urges to stop moving.
By long, slow distance, I mean mileages in excess of at least 15 miles at a time, and as you get in better shape, that number will creep up to 20 or 25, or more. By the time I am ready for my 50 mile trailrace in September, I expect to be running a 30 mile run on Saturdays and a 20 miler on Sundays, with max weekly mileage somewhere around 70-80.