An array of rf SQUIDs (Superconducting Quantum Interference Devices) in an alternating magnetic field can operate as a magnetic metamaterial where the phase and group velocities have opposite signs. In this system, discreteness and nonlinearity may lead to the generation of intrinsic localized modes in the from of discrete breathers. These breathers result from a balance of incoming power and losses, and they may change locally the response of a SQUID array to an applied field from diamagnetic to paramagnetic or vice-versa. We derive the dynamic flux equations for the damped and driven SQUID array and integrate them in the weak-coupling approximation to demonstrate the existence of various kinds of dissipative breathers. Besides using standard algorithms for breather construction, we have also observed the spontaneous breather generation in weakly disordered SQUID arrays. Moreover, low-energy breather-like pulses may be generated in end-driven arrays which propagate for fairly long distances in a dissipative environment. A short account on the tunability of the resonance of individual SQUIDs by application of either constant and/or alternating fields is also given.