I've recently replaced our antique Frigidare chest freezer, which died shortly after being moved to the house. A freezer definitely pays off for us in free food, plus the added bonus of being able to get bargains.
The freezer stores venison, gallons of wild berries, nuts (which don't have to freeze but keep better so I freeze them if there's space), etc. Plus homegrown vegetables (herbs I dry instead). I could get by without the freezer by canning the meat and veggies, but the berries would have to be canned in sugar, and I can cook healthier with frozen ones. Plus there's the cost of supplies (jars, lids, sugar, fuel to heat) and frankly, it's a lot more work. I think it would be cheaper and when I retire I may make the shift, after I run the numbers.
Then there are the storebought bargains: hams and turkeys at the holidays, 50 pounds of Vidalia onions every spring, bread from the day-old outlets which are too far away for regular trips, bushels of apples in the fall (missed that this year due to the freezer dying), etc. Basically, the freezer lets me buy a year's worth of food in season and eat at in-season prices all year. I'm fortunate that the old freezer died as a result of being moved; we'd been eating it down in preparation for the move and so I didn't lose a year's worth of food as I might have any other time.
I'll second the recommendation of a chest freezer over an upright, and manual defrost over frost-free. Cheaper to run and the food keeps better.