Mike Bullington, senior archives manager for McDonald's Corp., is a connoisseur of fast-food artifacts.

At work, he's surrounded by bags and packaging from years past. His cubicle holds a purse woven from Big Mac wrappers, a gift from a former chairman's wife, and a Ronald McDonald fashioned from Legos, turned in by a McDonald's franchisee. But the prize he treasures most recalls a menu item that had a brief stint in restaurants: Onion Nuggets, a precursor of sorts to Chicken McNuggets.

"Not...