Not all noise in experimental measurements is unwelcome. Certain fundamental noise sources contain valuable information about the system itself-a notable example being the inherent voltage fluctuations (Johnson noise) that exist across any resistor, which allow the temperature to be determined. In magnetic systems, fundamental noise can exist in the form of random spin fluctuations. For example, statistical fluctuations of N paramagnetic spins should generate measurable noise of order N spins, even in zero magnetic field. Here we exploit this effect to perform perturbation-free magnetic resonance. We use off-resonant Faraday rotation to passively detect the magnetization noise in an equilibrium ensemble of paramagnetic alkali atoms; the random fluctuations generate spontaneous spin coherences that precess and decay with the same characteristic energy and timescales as the macroscopic magnetization of an intentionally polarized or driven ensemble. Correlation spectra of the measured spin noise reveal g-factors, nuclear spin, isotope abundance ratios, hyperfine splittings, nuclear moments and spin coherence lifetimes-without having to excite, optically pump or otherwise drive the system away from thermal equilibrium. These noise signatures scale inversely with interaction volume, suggesting a possible route towards non-perturbative, sourceless magnetic resonance of small systems.