We demonstrate that textured closed surfaces, i.e., particles made of perfect electric conductors (PECs), are able to support localized electromagnetic resonances with properties resembling those of localized surface plasmons (LSPs) in the optical regime. Because of their similar behavior, we name these types of resonances as spoof LSPs. As a way of example, we show the existence of spoof LSPs in periodically textured PEC cylinders and the almost perfect analogy to optical plasmonics. We also present a metamaterial approach that captures the basic ingredients of their electromagnetic response.