Magnetic resonance spectra of EuTiO3 in both bulk and thin film form were taken at temperatures from 3-350 K and microwave frequencies from 9.2-9.8 and 34 GHz. In the paramagnetic phase, magnetic resonance spectra are determined by magnetic dipole and exchange interactions between Eu2+ spins. In the film, a large contribution arises from the demagnetization field. From detailed analysis of the linewidth and its temperature dependence, the parameters of spin-spin interactions were determined: the exchange frequency is 15-15.5 GHz and the estimated critical exponent of the spin correlation length is ~ 0.5. In the bulk samples, the spectra exhibited a distinct minimum in the linewidth at the Neel temperature, T_N = 5.5 K, while the resonance field practically does not change even on cooling below T_N. This is indicative of a small magnetic anisotropy ~ 320 G in the antiferromagnetic phase. In the film, the magnetic resonance spectrum is split below T_N into several components due to excitation of the magnetostatic modes, corresponding to a non-uniform precession of magnetization. Moreover, the film was observed to degrade over two years. This was manifested by an increase of defects and a change in the domain structure. The saturated magnetization in the film, estimated from the magnetic resonance spectrum, was about 900 emu/cm3 or 5.5 mu_B/unit cell at T = 3.5 K.