Just how dangerous is it to refreeze various foods?

I've heard it's ok to refreeze thawed meats as long as it was thawed in a cold environment. On the flip side, I've also heard casseroles, stews, lasagna and such should only ever be frozen once.

I end up wasting a lot of food, both raw and cooked, but following this advice. Is there actual science behind it, or is there relative safety in ignoring it as an old wive's tale?