For example, take a good hearty bowl of chili - the most common base ingredients include tomatoes, beans and ground beef. So for a heavy tomato sauce you would be on the search for a wine with a little less acidity and lighter on the tannin content. If your chili is heavy on beans or meat then you could also get away with a wine that has a bit more body and strength. Perhaps a Cabernet Sauvignon, Shiraz or a Malbec.
By taking these concepts a little further you can find the right wine match for a variety of soups, stews, chilis and chowders. Here are some pairings to get you started:
Chicken Noodle Soup would pair well with a Pinot Noir or perhaps a Chenin Blanc.
A Cream of Chicken Soup on the other hand would likely prefer a Sauvignon Blanc or Viognier.
If you are going for Gumbo consider a Pinot Noir.
For French Onion Soup give a French Beaujolais or Beaujolais Nouveau a go or perhaps opt for a White Burgundy.
If you are serving a Seafood Bisque or Stew you will want to grab a Sauvignon Blanc - the earthy tones, mixed with a citrusy spike will complement a myriad of sea creatures.
A hearty Chicken Tortilla Soup will appreciate a staple Spanish wine like a Rioja.
A New England Clam Chowder needs a well oaked Chardonnay. Speaking of chowder, perhaps you are a Corn Chowder fan, if so grab the nearest bottle of German Riesling (dry) and let it knock your socks off!
Keep in mind that there are no hard and fast rules for pairing wine with foods and specifically soups, stews and the like; however, there are certainly some wines that will enhance a pot of soup infinitely better than others. So experiment with some of these listings and try your own. If you find any tip top matches, be sure to share them on the wine forum.