What vegetable goes with prime rib?

Polenta would be nice change from potatoes. A creamy polenta.

Any kind of potato that will suck up the au jus or gravy.

My choice would be brased carrots with bibb lettuce, creamed spinach and mashed potatoes. I would
also make Yorkshire pudding or popovers.

Can Yorkshire pudding pass as a vegetable? No, okay then - add roast potatoes and carrots, and brussels sprouts. Some cliches are worth perpetuating.

Green beans and potato are classic as mentioned.
A rice pilaf, Caesar salad, Braised carrots, Or Stuffed mushrooms with quinoa, or stuffed mushrooms with spinach; Greek seasonings and feta cheese. (tho the stuff mushrooms could be bit to heavy to pare well).

I really like haricot vert with prime rib but it's really a matter of personal taste. Spinach is also good. Of course potatoes are a great match also, thats probably too obvious.