Time-of-flight and polarized triple axis neutron scattering is used to probe the spin excitations of Cu(DCOO)_2_·_4D_2O and La_2_-_xSr_xCuO_4. The first part of the thesis contains an investigation of the excitation spectrum of the square lattice S = 1/2Heisenberg antiferromagnet Cu(DCOO)_2_·_4D_2O. Along the antiferromagnetic zone boundary a pronounced intensity variation is found for the dominant single-magnon excitations. This variation tracks an already known zone boundary dispersion. Usingpolarization analysis to separate the components of the excitation spectrum, a continuum of longitudinally polarized multimagnon excitations is discovered at energies above the single-magnon branch. At low energies, the findings are well described bylinear spin wave theory. At high energies, linear spin wave theory fails and instead the data are very well accounted for by state-of-the-art Quantum Monte Carlo computations. In the second part of the thesis, the spin excitation spectra of the hightemperature superconductors La_1_._9_0Sr_0_._1_0CuO_4 and La_1_._8_4Sr_0_._1_6CuO_4 are characterized. The main discovery is that the excitations are dispersive at both doping levels. The dispersion strongly resembles that seen in other high-T_csuperconductors. The presence of dispersive excitations does not require superconductivity to exist. For La_1_._8_4Sr_0_._1_6CuO_4, but not for La_1_._9_0Sr_0_._1_0CuO_4, the onset of superconductivity gives rise to a spectral weight shift which displaysqualitative and quantitative similarities to the resonance mode observed in other high-T_c superconductors.