Are pilots generally trained for crosswind landings? A YouTube footage of a KLM Boeing 777 landing at Schiphol airport in the Netherlands is certainly scary as the plane bumps and weaves and rolls from side to side. 



Are pilots generally trained to handle such eventualities (or are such landings common in certain regions of the world?) or was everyone involved including the pilot taking a risk in this case without diverting the aircraft to a nearby safe location?
Of course yes.

Crosswind landings, like the one in the video you linked, are very common. In fact, landings with no wind or only headwind are rare.

There are several techniques pilots are taught during their extensive training to land aircraft when there is crosswind. The Wikipedia article I referenced above lists them. Since your question isn't about them, we won't discuss them.

Certainly, extreme weather situation are not very common. Some parts of the world experience extreme weather more than other areas. Diverting to other airports is not always an option and in some cases, once an airplane is on the approach, going around becomes impossible.