It depends 100% on why you are delayed.
If there is bad weather (and remember, even if it's fine where youa re, and fine where you're going, your plane might be coming from someplace it's not!), you are entitled to nothing.
If they've decided to cancel your flight because the King of Umblethwart wants to charter the plane and pay them $3 million for it, and they can rebook you on another flight(s) which get you in within two hours of the original arrival time, even if it means that instead of a non-stop you change planes twice, you get nothing.
On the other hand, if King Umblethwart charters that plane, and the options they offer you get you in two or more hours late, you are entitled to compensation which varies from carrier to carrier and the amount of time you are delayed. That compensation generallys tarts at vouchers worth $200, and goes up from there. BTW--You can always demand your ticket purchase price back in cash, and they have to give it to you.
Back in February I was on US Airways from Las Vegas to Newark with a change in Pittsburgh. On arriving in PIT my flight to EWR had been cancelled, as they decided to take the plane out of service for maintainence. They offered to put me on a flight to LGA then bus me over to EWR. That wasn't going to happen. Then they offered to put me up for the night in PIT and put me on the first flight to EWR the next morning. No dice. They offered me a flight on a competitor that I consider up there with Aeroflot. No way. I ended up on a flight to PHL and DH was able to pick me up there (I live 1/2 way between EWR and PHL, so it sisn't really matter). If I hadn't done that, and had ended up with one of the other options, I would have arrived over two hours later, and would have been entitled to compensation. I just wanted to get home
Anne