Many dissipative systems, most notably turbulent fluid flows, reach a well-defined steady state when they are maintained under constant out-of-equilibrium conditions. In most cases a mechanism for selecting this state (such as a minimization principle) is not known. In some spatially extended systems, the selected state is manifested as a pattern. I will discuss experimental results in two different areas: chemical pattern formation and the instabilities of flexible objects in a laminar flow (vortex-body interactions). I first present a study of rotating spiral waves in the Belousov-Zhabotinsky chemical reaction, focusing on the spiral selection problem, and the various pattern instabilities which we have observed. I discuss the implications for planned experiments on a chemical computer. Second, I present an experiment on the transition from fluttering to tumbling motion in falling paper. Finally, I will present preliminary results from an experiment on the motion of a flexible plate in an imposed flow, with direct relevance to the question of how fish swim.