In most reactions, especially in a biological environment, bonds are both broken and formed. The key to getting energy out of the system is to form stronger bonds than the ones you broke, this is certainly the case in the ATP --->ADP case you are talking about.
For example:
1/2
O2+H2 ----> H2O
The Oxygen molecule had a bon energy of 498kJ per mole, as we have 0.5 of a mole we use 249 kJ per mole to break the bond. For the hydrogen molecule the energy is 436kJ per mole. Therefore the total energy to break the bonds is 685 kJ per mole. The water molecule has two O-H bonds each with a bond energy of 427.6kJ per mole, total energy 855.2kJ per mole.
The energy released is therefore 855.2-685 = 170.2kJ per mole. So even though we broke some bonds the formation of the new bonds gives out more energy that the was used up in breaking the bonds in the first place. This is basic thermodynamics. There are some cases where other factors have to be considered, but I don't think that the ATP--->ADP will be one of them. Hope this helps, Hamish