We demonstrate a technique that enables ferromagnetic resonance measurements of the normal modes for magnetic excitations in individual nanoscale ferromagnets, smaller in volume by more than a factor of 50 compared to individual ferromagnetic samples measured by other resonance techniques. Studies of the resonance frequencies, amplitudes, linewidths, and line shapes as a function of microwave power, dc current, and magnetic field provide detailed new information about the exchange, damping, and spin-transfer torques that govern the dynamics in magnetic nanostructures.