The only one I like is asparagus. I have a bed of perennial onions (Top setting) but only as a novelty. Those I don't bother with altho they grow like weeds are Perpetual beets (Swiss Chard), Rhubarb, Jerusalem artichokes. More exotic perennials which I have not tried include Sea kale(Crambe maritime) Ground nut (Apios Americana) and Good King Henry (Chenopodium bonus-henricus) .

I grow Jerusalem Artichokes but there are several other veggies which, although not strictly speaking perennial, can go on for several seasons before conking out such as Chard, Wild Arugula and Kale. Then there are all the various perennial herbs ... and Rhubarb. You might also like to look at this thread from last year Perennial vegetables

If properly cared for, nightshade family plants are perennial for me. It's great! Pepper plants get huge and produce really well. Really nice to find ones I like, plant them and then just enjoy them instead of constant fussing.

Im wondering if Tronchuda kale will be perennial for me. My seedlings just made it through +115 temps so that seems promising. At least, it may live a good long while.

Asparagus and horseradish are the only perennial vegetables that I grow, but many of the nightshade family like cherry tomatoes and tomatillos readily volunteer so probably could get away without planting new ones each year if they were open pollinated varieties. I also only planted Dill one time in my garden and it just keeps coming up EVERYWHERE!

If you're in a warm enough climate. peppers are perennials. They are not frost tolerant, but with some protection, you can get them through nippy winters. Some question about whether over-wintered peppers are as productive. I had some jalapenos that did great in their second year, but in their third year, the plants were lush, but not as productive. Formally, tomatoes and eggplants are too, but I've never tried to overwinter them.

Buddies have "over wintered" eggplants and tomatoes and have been very pleased. Eggplants seemed to have been just as productive. Over wintered, as in it never froze. My tomatoes get to about a year and then something will happen, like heat death or foot rot from a downpour. I haven't had any production issues with my older pepper plants.

Mint, oregano and lemongrass are also perennial in the non-frost zones. So are the gingers. My galangal is finally doing decent.

Jerusalem artichokes escaped on me - I am still trying to eradicated them- Round Up may be next. Mint I am finally getting under control.

I have tarragon, rhubarb, oregano is literally everywhere (which I don't mind so much), chives, onion, and garlic. I love the tomato surprises and hope for them each year. Had some parsley spreading for a while but that has stopped.

Would like to have blueberries and strawberries and some fruit trees too. Oh have some wild raspberries and Day Lilies too - every part of the Day Lily plant is edible at different stages and take no care to grow.

Now also letting the Purslane grow too. Very easy and requires no care or watering. Oh I usu get some lettuce volunteers too but Purslane will take its place soon.