A great wine to pair with Brunswick stew is a dry white, such as Sauvignon Blanc or Pinot Grigio.  These light, acidic wines provide a refreshing contrast to the rich, flavorful stew.  You could also opt for an earthy red like Pinot Noir or Beaujolais to complement the smoky and spicy notes in the stew.  A chilled rosé can be another great option that brings out subtle flavors that might otherwise be overlooked.  When pairing, consider any additional ingredients in your Brunswick stew - such as tomatoes or corn - and choose a wine that will play nicely off those flavors.