A lot of dairy products become watery or start to separate if they've been frozen or defrosted: pastries with cream fillings, cream cheese, sour cream.
The USDA says does not recommend that eggs or canned foods be stored frozen. Eggshells can crack easily, and even if the shells remain intact, the consistency of egg yolks makes them difficult to use for anything other than hard-boiling. Canned foods that are frozen accidentally could pose health risks, so the USDA recommends inspecting to see if the can has rusted or burst. If the can is swollen, thaw it but check to make sure it doesn't look or smell off before eating.
The FDA also has a useful chart (pdf) on which foods don't freeze well and how long you can freeze other foods. (Note: when there is a recommended limit on how long a food should be frozen, it indicates when the quality of the food will decrease - NOT when it will "expire". You could theoretically freeze most foods indefinitely.)
The only other thing I would avoid freezing is any sort of raw green (lettuce, spinach, etc.). Greens wilt and turn brown when you freeze them. (If they're cooked, they should be fine to freeze and thaw.)
EDIT: Apparently, some spices become bitter when frozen, including pepper, cloves, garlic, green pepper, imitation vanilla, and onions, paprika and celery taste different.
Best Answer
They're often called ice spikes. Ten years ago these things were pretty mysterious, but now Wikipedia even has a video of them growing out of ice cube trays in a freezer.
Basically, the ice surface freezes first, which slightly pressurizes the water underneath. That water breaks through the crust, and continues to flow, and freeze to equalize pressure within the cooling cube. Temperature conditions have to be just right for it to happen, so you don't see them all the time.