I am a big fan of perennials because you can plant them once and they come back year after year. In our vegetable garden, the only perennial "vegetable" that we plant is asparagus. I love it because it is the first vegetable to come up in the spring and is pretty easy to grow and maintain.
Rubarb is another perennial, but I've always been afraid to grow it in our garden because the leaves are poisonous and my children are too used to eating everything out of the garden. But someday I'll add some.
Other than asparagus, we keep perennial berries in our garden - strawberries, raspberries, blackberries, blueberries, and (new to us) kiwi.
Even though it isn't a perennial, I will let some of my basil go to seed and it often comes back year after year.
The other self-sowing annual that we plant in the vegetable garden are orange marigolds. Marigolds can help repel bugs and the orange color is super cheery and makes me smile (not to mention the fact that it is a Goat Milk Stuff color). But the best thing about marigolds is that they are edible! I like to add some to salads. They brighten it up and make a wonderful talking point.
Perennials are a great investment and use of space in your garden. Do you plant any perennials?