There are some very comprehensive rules protecting European citizens when they travel around Europe. If the airlines fail to comply with these rules, they will be prosecuted and heavy fines are payable. So it's in your interests to know your rights. Let's start with the not uncommon situation of overbooked flights. You have paid for your ticket, you told the airline you were coming, and you present yourself at the airport on time only to find there are too many bodies waiting to get on the same flight. If this happens to you, the airline must first call for volunteers to give up their seats in return for agreed compensation. But suppose no one volunteers. Well, the choice falls to you.
If you decide not to travel, you are entitled to a full refund and compensation of up to 600 Euro. The actual amount varies depending on how long the intended flight and how many miles. But if it will still be worth traveling onward, you are entitled to be booked on to the first available flight to your destination. If you are offered a seat upgrade, the airline cannot ask you for the difference in price. If you must now break your journey and catch a connecting flight, all expenses must be met. Food and accommodation may also be necessary. Should the only available seats be in a lower class, you are entitled to a refund of the difference in ticket price.
As to cheap flights, particularly those booked as a package through a travel professional, you will be in line for significant compensation if you lose the benefit of car rental or hotel accommodation. If you did buy through a travel agent, the airline is obliged to compensate the travel agent and, in turn, the agent is obliged to pass on the compensation to you. If you have any complaint about the airline and the treatment you received when you were refused boarding, make a complaint to the National Enforcement Body in your home state. Officers are supposed to help you recover the full amount of compensation available under EU law.