Are there treatments for cancer that do not cause hair loss?

Sure, many of them: Not all cancer treatment will give you hair loss. Surgery and radiation therapy will not give you hair loss- unless if the radiation is directed toward your head. Some chemotherapy will cause hair loss- but not all of them. Nowadays, more biological/targetted therapy are available-eg. Herceptin, avastin, (bevacizumab) tarceva, gleevec, etc. Those biological/targetted therapy- will not give you hair loss.

Yes.: Hair loss during cancer treatment depends on the types of treatment being used. Many chemotherapy agents (not all) cause temporary hair loss, while radiation directed at the head may lead to a more permanent problem with higher doses. Unfortunately, when chemo is needed, you can't always choose just those medicines that don't cause hair loss because they may not work against that kind of cancer.