Cycles that are longer than the year, but less than 1000 years
The Moon does not follow the ecliptic precisely like the Sun does; rather, it follows a path inclined of about 5.14&deg;. The two points where the ecliptic and the Moon's path coincide are called 'nodes', and they travel around the ecliptic in a period of 18.66 years. This is a combination of the orbital period of the Moon, also called the sidereal month, about 27.32 days, and the slightly shorter draconic month, the average period between the moment where the Moon traverses a node, which is 27.21 days.

Once every 18.66 years, the ascending node coincides with the vernal equinox, and the Moon will reach declinations of about +28&deg; and -28&deg; (much more than the Sun, which reaches ±23&deg;); this is called a 'major lunar standstill'. 9.33 years later, the opposite is true, and the Moon will only reach ±18&deg; during a 'minor lunar standstill'.

According to Wikipedia these moments have had historical significance, all the way back to the Bronze Age:


  This time appears to have had special significance for the Bronze Age societies, who built the megalithic monuments in Britain and Ireland. It also has significance for some neopagan religions. Evidence also exists that alignments to the moonrise or moonset on the days of lunar standstills can be found in ancient sites of other ancient cultures, such as at Chimney Rock in Colorado and Hopewell Sites in Ohio.