I was also thinking Asparagus, but wasn't sure of another, so I did a search for perennial vegetables, and got a pretty long list:

Artichokes, Asparagus, Beans (perennials like scarlet runner), Broccoli (perennials like purple cape), Cannas (there are edible forms), Cardoon, Chard (perennial), Chicory, Chives, Chokos, Corn Salad, Dandelions, Fennel, French sorrel, Garlic Chives, Ginger, Good King Henry, Japanese hornwort, Jerusalem artichokes, Lemon Balm, Lovage, New Zealand spinach, okinawan spinach, Purslane, Rhubarb, Rocket, Sorrel, Sweet potato, sunchokes, Tamarillo, Walking Onions

If you live in warm climates, Okra will grow as a perennial; Mom grew up in Lousiana, and she said that it grew there as a perennial.