We demonstrate experimentally and theoretically that spoof surface plasmons (SSPs) can propagate without diffraction, i.e., self-collimation (SC) of SSPs. To excite and detect SSPs on a structured brass surface, we employed a pair of monopole antennas. The scanned horizontal and vertical field intensity distributions of the SSPs reveal a narrow Gaussian envelope at the SC frequency. While the Gaussian SSP is well maintained, being prevented from spreading during lengthy propagation, SSPs with frequencies below or above the SC frequency diverge. We examine the possibility of steering self-collimated SSPs.