Look into some of the species of ungulates on the African savanna. I believe, for instance that wildabeest and various species of gazelles/antelopes are known to demonstrate synchronized calving/breeding.
Birds that flock also demonstrate high levels of synchronization and schooling fish.
For insects, I would add periodic cicada emergences (some occurring over 17 year periods in the U.S.), migrating butterflies like Danaus plexippius, army/driver ants, termite emergences in Africa, "marching" activity in some caterpillars, etc. Surely there are many more examples...
Most social species exhibit behavioral synchronization (e.g., communal nesting in nursing in mice, grazing/foraging location, spacing, and movement in ungulates and primates, cooperative hunting in carnivores and cetaceans, etc.). Menstrual synchrony in humans is often brought up but is more likely an artifact of converging (and subsequent divergence) of asynchronous cycles.
Some bird flocks, such as starlings, demonstrate extraordinary synchronization of movement in flight. Here's a link to a scientific publication of the National Academy of Sciences of the United States, regarding starlings, and another to a general article about bird flocks in flight, from the National Audubon Society.
I am unclear about the type of synchronization that is of interest. I have observed chipmunks (Eutamias sp.) in British Columbia synchronize their daily feeding behaviour, presumably to increase vigilance for predators. This behaviour has not, to my knowledge, been properly documented.
Thank you very much for all your answers. It helps me a lot.
To your opinion, does grooming in monkeys could be considered as synchronized behaviour (e.g., two dyads of monkeys producing grooming at the same time) ?