This paper discusses a recent event in the western American power system when a forced oscillation was observed at a frequency that was close to a well-known 0.38-Hz inter-area electromechanical mode frequency of the western system. The event motivates a systematic investigation in this paper on the possibility of resonant interactions between forced oscillations and electromechanical inter-area oscillatory modes in power systems. When the natural oscillatory mode of a power system is poorly damped, and the forced oscillation occurs at a frequency close to system mode frequency at critical locations for the mode, resonance is observed in simulation test cases of the paper. It is shown that the MW oscillations on tie-lines can be as high as 477 MW from a 10-MW forced oscillation in Kundur test system because of resonance. This paper discusses the underlying system conditions and effects as related to resonance in power systems caused by forced oscillations and discusses ways to detect such scenarios using synchrophasors. Simulated data from Kundur two-area test power system as well as measurement data from western American power system are used to study the effect of forced oscillations in power systems.