Update: Added info about Zeolite-water ice makers and re-edited.
When your electricity fails, with it goes your ability to refrigerate. A well-insulated, full refrigerator will keep the perishable contents for perhaps 4 hours with the door kept shut. A full freezer should be fine for 48 hours. See Keeping Food Safe During An Emergency for further recommendations.
So, what can you do if power goes off for days or weeks? Well, you could use a propane refrigerator or if you would prefer to prepare ahead of time and like the notion of both independence and sustainability, you could try building a solar ice maker (pdf).