Any business that is considered a “place of public accommodation” is required to provide equal access to services under the nondiscrimination requirements of Title III of ADA. When you look at the guidelines closely, this includes hotels, entertainment venues, legal and accounting firms, retail stores, and virtually every business that is not a private club, including businesses that exist solely on the web.
The gray area is a matter of scale and purpose. If you have a small business which serves as specific market it's a good idea to make the site as user and disability friendly as possible. If, however, your market serves segments with a likeliness to have various handicaps or disabilities you should address that with an ADA Compliance review of the site. Also consider the scale and purpose of an organization. Publicly traded large businesses need to concern themselves more than a single location family owned retailer and if someone sues your flower shop because the text was too small or didn't have "image alt tags" causing them distress... That's pretty frivolous and would likely not stand.
Web designers often design in such a way that does not allow the user to adjust font size or color. While they may be protecting their brand, they are also inhibiting some users. Many visually impaired need to use high contrast color settings or very large fonts to read a website. Don't design your website in a way that makes it impossible for them to do this. 

The good news for potential defendants is that the only remedies available in private ADA suits are injunctions that force you to come into compliance and attorneys’ fees. If the Department of Justice gets involved, they can seek civil fines and penalties. Hence, you need to do the risk/benefit analysis as to whether it is worth challenging the claim or not. This report says the lawsuits are on the rise.
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.”
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