Harnessing snapping, an instability phenomenon observed in nature (e.g., Venus flytraps), for autonomy has attracted growing interest in autonomous soft robots. However, achieving self‐sustained snapping and snapping‐driven autonomous motions in soft robots remains largely unexplored. Here, harnessing bistable, ribbon ring‐like structures for realizing self‐sustained snapping in a library of soft liquid‐crystal elastomer wavy rings under constant thermal and photothermal actuation are reported. The self‐sustained snapping induces continuous ring flipping that drives autonomous dancing or crawling motions on the ground and underwater. The 3D, free‐standing wavy rings employ either a highly symmetric or symmetry‐broken twisted shape with tunable geometric asymmetries. It is found that the former favors periodic self‐dancing motion in place due to isotropic friction, while the latter shows a directional crawling motion along the predefined axis of symmetry during fabrication due to asymmetric friction. It shows that the crawling speed can be tuned by the geometric asymmetries with a peak speed achieved at the highest geometric asymmetry. Lastly, it is shown that the autonomous crawling ring can also adapt its body shape to pass through a confined space that is over 30% narrower than its body size. Achieving self‐sustained snapping and motion remains challenging in autonomous systems. Harnessing wavy ribbon rings for realizing self‐sustained snapping in liquid‐crystal elastomer rings under constant temperature and light are reported. It drives continuous flipping for either periodic self‐dancing in place in symmetric rings or self‐crawling in asymmetric rings on the ground and underwater, as well as self‐escaping from confined spaces.