We have measured the internal friction (Q-1) of amorphous silicon nitride (a-Si3Nx) films prepared by a variety of methods, including low-pressure chemical-vapor deposition (LPCVD), plasma-enhanced chemical-vapor deposition (PECVD), and hot-wire chemical-vapor deposition (HWCVD) from 0.5 K to room temperature. The measurements are made by depositing the films onto extremely high-Q silicon double paddle oscillator substrates with a resonant frequency of ~5500 Hz. We find the elastic properties of these a-Si3N4 films resemble those of amorphous silicon (a-Si), demonstrating considerable variation, depending on the film growth methods and post deposition annealing. The internal friction for most of the films shows a broad temperature-independent plateau below 30 K, characteristic of amorphous solids. The values of Q-1, however, vary from film to film in this plateau region by more than one order of magnitude. This is typical for tetrehedrally bonded amorphous thin films, like a-Si, a-Ge, and a-C. The PECVD films have the highest Q-1 just like an ordinary amorphous solid, while LPCVD films have an internal friction more than one order of magnitude lower. All the films show a reduction of Q-1 after annealing at 800°C, even for the LPCVD films which were prepared at 850°C. This can be viewed as a reduction of structural disorder.