The vegetables that I like to use in my beef stew are potatoes, carrots, and celery. Turnips go great as well as parsnips, and of course, adding onions or garlic is always a good idea. I finished this with some mushrooms for a bit of an earthy flavor. I think this is a perfect combination and they go so well together. But you can really use any vegetables that you like or have on hand. Some other vegetables that would be good in this stew are peas, corn, or even green beans. Just throw in whatever you like or have on hand. The great thing about beef stew is that it is very versatile.