That's interesting-as a white female it is a non issue. It would be a different kettle of fish if I weren't as there are benefits to being an original inhabitant. In the 10 yearly census, many people identify as Jedi knight.
I usually write in AMERICAN. I know that's not a race but it's all they need to know. My father I think is mostly Irish my mother is Portuguese. Different races label me differently. In the bay area I was a white boy. Now I live in a predominantly white town and people of color tell me I'm not white. Go figure. I'm AMERICAN.
They usually ask about race for reporting reasons, not because it's necessarily relevant to the task at hand. It's how we get data on racial breakdowns in all sorts of areas. By answering "other", you're diluting the quality of that data. Not that big a deal. Just an FYI.
Always truthfully for official forms. If its not an official organization (health, government, or education) and not mandatory I'd leave it blank, not sure why they'd care except to target me for a consumer group. If it was mandatory for a non-official group, I might not fill out the form at all.