Just a poll for your polling pleasure.
Celery is disgusting.
Well, you definitely need your standard mirepoix (carrots, celery, and onion). I will accept celery root/celariac in lieu of celery stalks. After that, it’s up to you, but generally I want to also see potatoes in there, and maybe some parsnip. I generally do not use green beans, peans, or lima beans (and have never used corn.)
Celery or celeriac is essential for most Western style soups. Carrots and onions (or spring onions) I like.
For Thai style soup: you can leave out the celery, but you must add ginger and lemongrass and probably fish sauce.
Everything else is optional, but potatoes or parsnip are nice.
Possible alternatives include barley and turnips, though my roomie likes parsnips. No mushrooms allowed, I am deathly allergic.
herbs: bay leaf, rosemary, thyme, marjoram and black pepper. Salt is added to taste, at least a tiny pinch.
The beauty of vegetable beef soup is that you can use whatever veggies you like or have on hand. I voted for all of them. 
I think the first four ingredients (mirepoix plus potatoes) are essential. The rest are optional (though a tomato base is very common). There’s nothing wrong with any of the other ingredients, it’s just about throwing in whatever you’ve got on hand at that point. I like to throw in barley myself. Asparagus and okra can also be interesting additions.
Any vegetables are fine, except lima beans, which should be eradicated from the planet, including any cultivars or other variations which could be used to regenerate the line. Any remaining traces of lima beans, along with ten feet of soil removed from any land ever used to grow lima beans, should be incinerated in an underground nuclear explosion.
Whatever you’ve got on hand. Isn’t that half the purpose of soup?
Other: Swede or Turnip.
ETA: Beer. What do you mean it’s not a vegetable? Made from grain… an’ stuff…
I vote for everything except lima beans, although corn is a bit of a stretch. I think broccoli, while not the most fitting ingredient, fits a bit better than corn.
I just made some a few days ago!
In mine went:
- beef stock, homemade, out of the freezer.
- leeks, because leeks are better than onions in soup. WAY better.
- carrots, because Mr. Athena loooooves carrots.
- leftover pot roast from a few days previous.
- leftover parsnips and potatoes from pot roast.
- leftover juicy goodness from pot roast.
- kale, because kale in soup is yummy.
- a can of white beans, because I wanted something starchy and there were only a couple leftover potatoes. The other option was barley but bean sounded better this time.
- A can of diced tomatoes, for the acidity.
- NO celery. Yuk. I don’t like celery in soup.
I think that’s it, but I may remember more. I pretty much do what Ruby said and just used what I had in the fridge, though I did go out and buy kale especially for it because it’s just that good.
All of the above except corn and lima beans. Actually, peas are optional (fine with or without).
I just made some myself!
Homemade vegetable stock
onions
carrots
celery
the above three vegetables being the classic mirepoix
green beans
turnips
rutabagas
parsnips
kale
potatoes
zucchini
Rancho Gordo Ayocote Morado (purple runner) beans
yellow squash
tomatoes
garlic
and herbs:
parsley
marjoram
oregano
thyme
rosemary
savory
Virtually anything in mine, except brocolli (too bitter) or squash/zucchini (too mushy, in my opinion.) The whole point of veggie beef stew is to use up the bits and dabs of leftover vegetables in the refrigerator, right? But my family would riot if the first five ingredients, plus corn, weren’t somehow involved in making this type of soup.
I’ll add that if I want to make my veggie soup NOT vegetarian, I’ll sauté up and add some sliced Italian sausage…
I just went with which ones I’d never had in soup, thus not voting for peas or lima beans. I also unvoted celery, but I do like adding it for flavor, but not as a vegetable in it’s own right. It’s more part of the proper seasoning for the beef. Mushy celery tastes bland, which is almost worse than raw celery.
It takes all kinds of vegetables.
All kinds of vegetables.
Parsnips, carrots, turnips and onions.
Throw a swede in for those so inclined…