When did the last rifting / break-up event occur?
Rifting is an ongoing process. At the moment, e.g. East Africa is rifting apart from the Nubian plate, we also see rifting of continental plates elsewhere, eg Rio Grande. New continents are being formed, but it doesn't happen on a human time scale. Modellers of future geography have a difficult task to decide what rifts that will stop and what rift that eventually will result in a new continent. 

See yellow marked faults and rifts:


Madagascar is sometimes refereed to as the eight continent, not only of biogeographic reasons. It was rifting away from Africa and later India during mesozoic time, starting 160 Ma. 

The last rifting that resulted in the present continents I can think about (probably the community can come up with a later event!), would be the North Atlantic breakup, that is still ongoing, but the last part of separation of present continents was the opening of the Fram Strait 16-10 Ma. This separated Greenland from the European plate and had a large impact on the Arctic Ocean conditions.