State law varies on this issue. I would contact your state's department of labor.

I am no legal representative, but I know that morally you should be paid for that time, being in that position meant that you had to be around to answer calls at all times, which means that going out for the evenings with friends would be interrupted, going to the cinema would be interrupted and I think it would be wrong not to get paid a set amount for the time lost

I believe you should be. I mean you're expected to drop anything else when you answer the phone so i dont see why you wouldn't get paid for that time. But like WRG said, unfortunately it's the laws that dictate whether or not you should be paid.

Although state law may vary, Federal law says you only have to be paid for: a) the time you were actually working, or b) the time you were obligated to be at a specific place or within a specific traveling distance from work. In your case, having to carry a phone did not obligate you to stay within say a 20 minute radius (response time) of your employment location, so under that definition, you were not required to be paid. Outside of possibly a movie, I don't see how you were limited in your choice of personal activities (and even at the movies, you could put the phone on vibrate).

Each company has in place their policies on payment for certain situations. In one company I worked for as a claim adjuster they would rotate the phone to each adjuster for a week to take calls at home from policyholders who had accidents that we would set up a claim for and follow up with the following day. In some weeks might get no calls a night or could get 20, especially on the weekend when the majority of most accidents happen. We were paid $100 for the entire week if we got no calls or 50.

Granted it can be an inconvenience since you think ahead to what you might do on your personal time and hope no one calls or if asleep, hope not to be waken up for a call.

So it appears you no longer work there and it is doubt-full that they would have been required to pay for your down time, but only for the time it took to take care of business period. This company provided a service to their clients by having someone available to take their calls when needed.