A motile cell, when stimulated, shows a dramatic increase in the activity of its membrane, manifested by the appearance of dynamic membrane structures such as lamellipodia, filopodia, and membrane ruffles. The external stimulus turns on membrane bound activators, like Cdc42 and PIP2, which cause increased branching and polymerization of the actin cytoskeleton in their vicinity leading to a local protrusive force on the membrane. The emergence of the complex membrane structures is a result of the coupling between the dynamics of the membrane, the activators, and the protrusive forces. We present a simple model that treats the dynamics of a membrane under the action of actin polymerization forces that depend on the local density of freely diffusing activators on the membrane. We show that, depending on the spontaneous membrane curvature associated with the activators, the resulting membrane motion can be wavelike, corresponding to membrane ruffling and actin waves, or unstable, indicating the tendency of filopodia to form. Our model also quantitatively explains a variety of related experimental observations and makes several testable predictions.