We study a free scalar field ϕ in a fixed curved background spacetime subject to a higher derivative field equation of the form F(□)ϕ=0, where F is a polynomial of the form F(□)=∏i(□-mi2) and all masses mi are distinct and real. Using an auxiliary field method to simplify the calculations, we obtain expressions for the Belinfante-Rosenfeld symmetric energy-momentum tensor and compare it with the canonical energy-momentum tensor when the background is Minkowski spacetime. We also obtain the conserved symplectic current necessary for quantization and briefly discuss the issue of negative energy vs negative norm and its relation to reflection positivity in Euclidean treatments. We study, without assuming spherical symmetry, the possible existence of finite energy static solutions of the scalar equations, in static or stationary background geometries. Subject to various assumptions on the potential, we establish nonexistence results including a no-scalar-hair theorem for static black holes. We consider Pais-Uhlenbeck field theories in a cosmological de Sitter background and show how the Hubble friction may eliminate what would otherwise be unstable behavior when interactions are included.