A good or excellent credit score makes you look less risky to companies. If you have a 750 score, you can probably ask for no fees when you open bank accounts, credit card accounts, and even utility lines.
A great credit score will also encourage lenders and investment brokers to charge you lower fees and interest rates. If you have a low credit score, work to build it as quickly as possible. A great score will save you money throughout life.
Not sure how to avoid fees for some services and products? Pick up the phone and ask. You never know what response you will get.