How to get by without a refrigerator (i.e. the lessons we learned the last week and a half):
1. Soy Milk. This is a trick I learned in college: buy soy milk in cartons and until you open them their shelf life is virtually forever. I know it doesn't taste quite the same as milk but it'll do in a pinch (and it works just fine for baking). We've found that even an open container of soy milk lasts quite a while at room temperature (as in 1-5 days depending on how warm the room is), and you can buy individual sized ones if you don't want to take any chances.
2. Yogurt. Yogurt is made at room temperature, so if you don't refrigerate it, your yogurt just gets more yogurt-y. The bacteria that make the yogurt are good and produce a lot of acid that other bacteria can't grow in, so that helps preserve it (although not forever). Usually the yogurt gets too yogurt-y before it goes sour (e.g. soupy and curdy).
3. PB&J. This is our favorite lunch staple and in an emergency works for dinner too. Peanut butter and jelly are both sterile when you open them and are naturally preserved by the salt and sugar in them (yes sugar, in high concentration, acts as a preservative - this is why pie and other desserts can be kept out of the refrigerator).
4. Canned tuna (and other meat). This one seems obvious but didn't occur to us until a few days in. With pasta and tomatoes, it makes a completely refrigerator-less meal. Be sure to eat it all up though!
5. The grocery store is your friend. If you live near a grocery store (as we do) you can plan your running route past it, walk there after work, or just plain drive up there real quick before dinner and buy everything you need right before you're going to cook it. Go ahead and get friendly with the checkers there because you're going to be seeing a lot of them.
6. The burrito stand on the corner is yummy and won't poison you. Even though it looked like a ghetto burrito stand that is not to be trusted, we gave it a shot and it turns out it's great. And the burritos are only $4!
So with a few strategic adjustments, we've managed to get by. Supposedly we're finally getting a new fridge tomorrow. If not, I'm hiring a lawyer AND moving out. This is the negative of renting: when the refrigerator breaks you are dependent on someone else to get you a new one, and they can take however long they want (although the law says they can only take 72 hrs, hence the planned lawsuit).