While almost any vegetable can be put into soup, some have characteristics that may make your vegetable soup less appealing. Here's a short list of some you may want to avoid: beets (unless you're making borscht), Brussels sprouts, artichokes, winter squash (unless you're making squash soup), lettuce or other tender greens, mustard greens or other strong-tasting greens. If you're planning on freezing the soup, avoid potatoes or sweet potatoes because they tend to get mushy when frozen.