I've lived without using a fridge for about a year now. Not difficult. Just don't buy food that needs refrigeration. Cook in small enough batches so there is no leftovers. Use cheap fuel sources for cooking if you plan to can food yourself. Be careful though to follow the latest guidelines on canning/drying/curing/etc or you may end up dead.
In the summer time I do use an ice cooler sometimes to keep the odd treat cold or keep some drinks cold. I can fill the chest for a couple of dollars and it lasts a week. However from a simple cost point of view, it's cheaper for me to use a fridge. Would only cost me about $5 a month to run a fridge. I just don't use a fridge enough to warrant leaving it running all the time (yes I do have a fridge, just don't use it). In the winter I just leave what I want to keep cold outside or in a closet that is against an exterior wall. Typically all I ever need to keep cool is the occasional "drink".
If you want a really efficient fridge and don't mind a little work, here's what you do. Get a cheapo working chest freezer. Salvage the guts of it. Build a custom "box" to replace the crappy box that came with it. Think 4in or so of foam. Mate the guts to the new box and use a thermostatically controlled outlet that has a remote sensor to control the guts. If you are feeling brave, you could probably do it another way. Never tried it but have heard plenty of people doing similar. Most times though they just get a chest freezer, add extra insulation, and put it on a thermostatically controlled outlet.
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