We studied various characteristics of the flow-induced vibration (FIV) of a spring-mounted cylinder, and the fluctuating lift and drag forces exerted on the cylinder due to the periodic changes in the fluid motion and vortex structure. We compared two conditions, which represent the limiting cases for the solid-to-fluid density ratio: the cylinder density is negligible relative to the fluid density, and the fluid density is negligible relative to the cylinder density. For both conditions, we examined the changes in these characteristics over a wide range of nondimensional mass-damping for one degree of freedom (1-DOF, cross-flow) and 2-DOF (cross-flow and in-line) vibration. The four cases exhibit differences (especially at low mass-damping) but also have some similarities in the characteristics of the FIV, induced forces, and energy extraction from the flow. We examined these differences and similarities, the implied errors when the in-line DOF is neglected, and the feasibility of using a single mass-damping parameter to describe the FIV.