The Super Wide Angle Search for Planets (SuperWASP) is a whole-sky high-cadence optical survey which has searched for exoplanetary transit signatures since 2004. Its archive contains long-term light curves for ~30 million 8-15 V magnitude stars, making it a valuable serendipitous resource for variable star research. We have concentrated on the evidence it provides for eclipsing binaries, in particular those exhibiting orbital period variations, and have developed custom tools to measure periods precisely and detect period changes reliably. Amongst our results are: a collection of 143 candidate contact or semi-detached eclipsing binaries near the short-period limit in the main sequence binary period distribution; a probable hierarchical triple exhibiting dramatic sinusoidal period variations; a new doubly-eclipsing quintuple system; and new evidence for period change or stability in 12 post-common-envelope eclipsing binaries, which may support the existence of circumbinary planets in such systems. A large-scale search for period changes in ~14000 SuperWASP eclipsing binary candidates also yields numerous examples of sinusoidal period change, suggestive of tertiary companions, and may allow us to constrain the frequency of triple systems amongst low-mass stars.