I have heard the claim that "Ocean waves travel in groups of seven, and the seventh wave is the biggest of the bunch." Is this fact of fiction?
NO, the wave weather is called "superposition of waves with random periods/frequencies and directions" for a reason.
This answer was already addressed, but with a 9 instead a 7 here in Skeptics SE, the remarkable part is... (notes in bold)
In the fetch, many different groups of waves of varying wavelength are generated and interfere (noted in the literature as sea state). As they disperse away from the fetch, the waves become more regularly sized and spaced (knows as swell state). This is because the speed of a wave in open water is closely related to its wavelength. The different groups of waves move at different speeds and so are naturally sorted by wavelength.
with lead to the same answer with another number:
Even when is possible for two wave trains (generated by two diferent storms or conditions) to converge (as the largest, fastest-moving waves at the fore of the second train can "catch", the smaller, slower-moving ones behind of the first train) or the sorting of wave frequencies as described above, generate waves coupling that can be interpreted as this "Xth wave" this effect is accidental due the difficulty of measure wave height at naked eye, variability of amplitude of wave and phasing of waves ratios and due the fact the most wave have periods between 8 and 26 seconds and is extremely hard get in the sea periods ratios of 7 to 10 to generate this "Xth wave".
I hope this helps