There have been people living on the Island for an undetermined amount of time. Remains have been found which could date back to the 1800s. The US Army, a French science team (Rousseau), a drug smuggler, Henry Gale, Naomi, the Dharma Initiative, and Desmond have arrived on the Island at different times and by different means, some on purpose and others by chance. It seems as though people that lived on the Island in a different period of time and left the island, but came back, experience nosebleeds during the time shifts and could possibly die unless they find a "constant" or someone to connect to in the future. Daniel Faraday knows all about this.
Benjamin Linus, or better know as Ben lied about being born on the Island. He was born in the woods near Portland, but he came to live on the Island as part of the Dharma Initiative in the 70s. Sayid almost kills Ben in a time flash. Very confusing. I still cannot understand his motives, but he is evil.
Miles Straume was not born on the island either, but was raised there as a baby during the Dharma Initiative. He left with his mother and lived in California. He came back on the Kahuna freighter. He also experienced nosebleeds during the time flashes. He has to the ability to communicate with dead people.
Richard Alpert has been on the Island for who knows how long. He is the leader of the "Others". He does not age. He may have a different hairdo in different episodes, but he looks the same. Apparently he was given this gift by Jacob who also does not age. That's Daniel's mother Eloise with Richard.
Danielle Rousseau. She came in 1988 on a raft with 6 others from a French science expedition. She was 7-8 months pregnant. She eventually became the only survivor of this group. She gave birth to Alex by herself and lived in isolation for 16 years sending out a distress call until Oceanic 815. She is one tough cookie. Her story is told in Season 5 - "The Little Prince."