What about Marking "Other"?
If you think your ethnicity deserves more attention than implied by the word "Caucasian," you can mark "other." It might get you past presumptive deny at a few schools. or it might make no difference at all. Recent immigrants from Europe might benefit from this.
If you're doing it merely as a matter of ethnic pride, go ahead. Many applicants (my niece and myself included) don't think "White" does justice to our ethnic mix, of which we are proud. But don't expect it to give you any advantage in the admissions process, unless your personal statement focuses on your ethnic background and is interesting. In other words, which box you check won't matter unless you have other material in the file to back it up.
Whether or not your ethnicity matters to you, it matters to the Department of Education these days; they've added more categories than you can imagine to the LSAC reporting guidelines -- look!
So where IS "Other"? There are several of them -- other white, other Asian, other Hispanic, and other Canadian Aboriginal. Surely one of them describes you.