I heard both many a time, but my vague memories suggest I used to hear *two-dimensional *more often and only in the last ten, fifteen years has *one-dimensional *fallen into vogue. Seems to me calling a character two-dimensional pretty much covers the notion that they have no depth and using *one-dimensional *is overkill - like saying, “he’s reeeeeeeeeeeeeeaaaaaallly two-dimensional!”
But lacking an OED to look into origins, I make the plea for help.
It’s clear what the internet prefers. Google “two-dimensional character” and get 272,000 hits. Google “one-dimensional character” and get 2,560,000 hits. But is one more proper than the other? And which came first?