Although most people serve or eat bread with soup you can eat anything else alongside soup.
Some other foods that go well with soup besides bread are foods such as potato puffs, roasted broccoli, roasted garlic, bread sticks, celery sticks, celery and carrots.
Also Tortilla Chips or any other chips go well with soup.
I also like to eat some sausage links along with soup especially if I eat some soup for breakfast.
Sausage and soup goes well together.
Toast and soup is also good but it's bread and you could make cinnamon toast to eat along with the soup.
Even eating some cheese such as string cheese goes well with soups.