All corporations must register with every U.S. state in which the corporation conducts business. This registration process is often called "foreign qualification" because a corporation is a "foreign" corporation in every state other than the state where it is incorporated.
At initial formation, this means that a Delaware startup must typically foreign qualify at least in the state where the startup has its principal place of business. For a startup, the principal place of business is usually where the founders are located and is often the home of one of the founders.
Even if a Delaware startup offers an exclusively online service, it almost certainly must foreign qualify with at least one state (except in the rare case where the startup's founders actually work only in Delaware or only outside of the United States). Logically, every startup must have a "principal" place of business, which is generally the startup’s headquarters or nerve center (the place where the startup’s officers direct, control, and coordinate the startup’s activities). And, regardless of where a startup offers its service, the conduct of its other business affairs is, in aggregate, likely to require that the startup register to conduct business in the state where its principal place of business is located.
Consequences for conducting business before foreign qualifying vary from state to state. For example, possible consequences if a Delaware startup does business in California before foreign qualifying include:
Consult an attorney if you have questions about your specific circumstances.