Corn would have to be high on the list because it's so useful, flexible, and goes with so much. You've got corn kernels, cornmeal, grits, hominy. You can use it in any course of the meal, and add it to almost any dish. Corn is a workhorse.
The chile pepper might arguably be the vegetable I rely on the most, though. Certainly high on the list.
Somewhere in there I'd have to include okra, fresh fava beans (sadly, canned and dry do not show up anywhere on the list), cucumbers, potatoes, garlic, beets, radishes for about two weeks a year (they're fine year-round; they're spectacular fresh from the dirt), and greens of all kinds.
Purslane is on the list, and the newest addition thereto. Nothing else is quite like purslane. It's an invasive weed, and people may be surprised to see you (i.e. me) growing it on purpose. They say it'll take over your garden, and God I hope so -- my front yard is hostile to gardening, repelling most of the things I try to grow there; only equally invasive mint has flourished, though peppers and tomatoes do all right in a good year. (This is not a good year, and if it doesn't stop raining, my pimiento peppers won't ripen, and I WILL BE VERY DISPLEASED ABOUT THAT.)
This is my biggest purslane plant, growing in a container on the deck. Brought it inside so I could trim some of it for lunch (with ribeye steak, sriracha, and bourbon-barrel-aged soy sauce).
As you can see, it's raining today. Again.
Purslane has a definite green taste, but it's distinctly different from greens like collards, spinach, etc. The leaves are very slightly mucilaginous inside -- not to the extent of okra, but enough that cooked purslane is used as a thickener. They're succulent -- you're not chewing a dry leaf, here, you could probably juice these things. They're also tangy -- from barely-noticeably-so to downright sour, depending on the weather and/or the time of day. I haven't actually figured out yet, what corresponds to the tanginess -- but I can tell you that today, very warm, rainy, cloudy, mid-day, the purslane was at the mild end. (I've wound up not trimming any to freeze, for that reason.) At its tangiest, you wouldn't want to add much vinaigrette to a purslane salad.
I haven't even tried it cooked yet. I'll blog about it when I do.