Observations of the Zeeman effect in OH and H2O masers provide valuable information about magnetic field strength and direction, but only for the very high density gas in which such masers are found. In order to understand the role of magnetic fields in the evolution of the interstellar medium and in the star formation process, it is essential to consider the maser results in the broader context of magnetic fields in lower density gas. This contribution will (very briefly) summarize the state of observational knowledge of magnetic fields in the non-masing gas. Magnetic fields in H I and molecular clouds may be observed via the Zeeman effect, linear polarization of dust emission, and linear polarization of spectral-line emission. Useful parameters that can be inferred from observations are the mass-to-flux ratio and the scaling of field strength with density. The former tells us whether magnetic fields exert sufficient pressure to provide support against gravitational contraction; the latter tells whether or not magnetic fields are sufficiently strong to determine the nature (spherical or disk geometry) of the contraction. Existing observations will be reviewed. Results are that the strength of interstellar magnetic fields remains roughly invariant at 5-10 microgauss between densities of 0.1 cm-3 < n(H) < 1,000 cm-3 but increases proportional to approximately the square root of density at higher densities. Moreover, the mass-to-flux ratio is significantly subcritical (strong magnetic support with respect to gravity) in diffuse H I clouds that are not self-gravitating, but becomes approximately critical in high-density molecular cloud cores. This suggests that MCs and GMCs form primarily by accumulation of matter along magnetic field lines, a process that will increase density but not magnetic field strength. How clumps in GMCs evolve will then depend crucially on the mass-to-flux ratio in each clump. Present data suggest that magnetic fields play a very significant role in the evolution of molecular clouds and in the star formation process.