It depends on the application. In a radio antenna it's a good thing, in a bridge it typically is not.
Resonances are typically frequencies where energy is easily coupled into the system. Depending on the application, this easy coupling of energy can be good or bad. When we want to couple energy into a system, say in the case of an antenna, resonances are desirable, whereas if we want do dampen out energy in the case of anti-vibration table, resonances are bad news. Sometimes systems can exhibit multiple resonances, which is usually a bad thing no matter what, because a system that is jumping between resonances is usually rather unpredictable. Any multimode laser is a good example of where this occurs.
