When the earliest human migrations occurred depends on your definition of the word "human", which, unfortunately, is not pinned down, in dictionaries or anywhere else. "Human" has at least two meanings: any member of the genus Homo, including Homo erectus, Homo habilis, et al, or only members of the species Homo sapiens.
The first members of the genus Homo, represented by Homo habilis ("handy man") evolved in Africa 2.4 million years ago (not 2.0 million years ago as is commonly stated). The main habitat of Homo habilis was South and East Africa. Around 1.9 million years ago, a larger-brained, more resourceful species of human evolved in Africa, Homo ergaster ("working man"). It is believed that Homo ergaster may have been one of the first members of the genus Homo to cross the Sinai Peninsula into the Middle East and on into the far East and the borders of Europe. Quickly after leaving Africa, H. ergaster probably evolved into Homo erectus, and H. erectus is often accordingly called the first member of the genus Homo to leave Africa. Some scientists consider H. ergaster and H. erectus to be members of the same species.
The spreading of Homo from Africa is partially explained by an idea called the Sahara Pump Theory. According to the geological evidence, around 2.0 million years ago, the Sahara was a wetter place, and flora and fauna were common. It was not a practically uninhabitable desert as it is today. This would have given an incentive for human migrations to move north, eventually crossing the Sinai Peninsula into the Levant.
Homo erectus lived in China and Southeast Asia at least 1.7 million years ago, based on stone tool findings. Most scientists do not believe H. erectus had the ability to build rafts and sail the oceans, so its migration patterns and limited to land travel only. Other homonids, such as H. antecessor, other members of Homo that might be called cousins of H. erectus, made it to Europe between 0.9 and 1.2 million years ago, where their fossils have been found in Spain and Italy.
Modern human migrations began about 70,000 years ago, when Homo sapiens wandered into the Levant and modern Yemen. Europe was colonized by 50,000 years ago, Australia by 40,000 years ago, and East Asia by 30,000 years ago. The colonization of Australia is notable because Homo erectus was incapable of sailing across the sea to reach it. Humans made it into the Americas via the Bering land bridge, but the exact date is under dispute: it may have occurred 30,000 years ago, or as recently as 14,000 years ago.
Human migrations have continued to this day. Polynesia is one of the latest areas to be colonized historically, with most of it only reached 3,000 years ago. New Zealand was colonized just 1,000 years ago. The first Antarctic base, "Little America" on the base on the Ross Ice Shelf, was established only in 1929. Further human migrations may consist of colonizing the ice sheets, the oceans, low Earth orbit, the Moon, Mars, and beyond.