By means of first-principles calculations, various properties of SrRuO3 are investigated, focusing on its lattice dynamical properties. Despite having a Goldschmidt tolerance factor very close to 1, the phonon dispersion curves of the high-temperature cubic phase of SrRuO3 show strong antiferrodistortive instabilities. The energetics of metastable phases with different tilt patterns are discussed, concluding that the coupling of oxygen rotation modes with anti-polar Sr motion plays a key role in stabilizing the Pnma phase with respect to alternative rotation patterns. Our systematic analysis confirms previous expectations and contributes to rationalizing better why many ABO(3) perovskites, including metallic compounds, exhibit an orthorhombic ground state. The zone-center phonon modes of the Pnma phase have been computed, from which we propose partial reassignment of available experimental data. The full dispersion curves have also been obtained, constituting benchmark results for the interpretation of future measurements and providing access to thermodynamical properties.