You probably won't have to check your site with all of the available evaluation tools out there, but it is a good idea to do so for the most common web browsers. Just as accessibility software makes it easier for people with disabilities to navigate the Internet, these tools make it easier for developers to ensure accessibility from the start. When you think you've mastered it, go back through the Section 508 compliance checklist to ensure you've met every goal.
Most recently, however, pizza chain Domino's has been brought under suit for their website not being accessible for specialty ordering. The U.S. Supreme Court refused to review the case, instead upholding the decision of the 9th U.S. Circuit Court of Appeals who said the “alleged inaccessibility of Domino’s website and app impedes access to the goods and services of its physical pizza franchises—which are places of public accommodation.”