Depends on the route. For domestic flights, nothing. If your delay is overnight, the DL Contract of Carriage (available online) states they will put you up in a hotel at their expense since the delay is not Force Majeure (like weather/ATC). But beyond that, there are no US regs or DL CoC terms that require they you give any compesation. If you happen to be flying from EU to US on DL (but not reverse), then EU261 delay compensation regulations would come into play.