According to Dr. Marvin Candle on the Orientation film (Ep: 2x3, Orientation):
The Dharma Initiative was created in 1970, and it is the brainchild of Gerald and Karen DeGroot -- two doctoral candidates at the University of Michigan following in the footsteps of visionaries such as B.F. Skinner.The Dharma logo shows up in many places around the island, including on the shark that Michael shot! (Ep: 2x2, Adrift) Lostpedia shows all of the Dharma logos.
In the second issue of Lost: The Official Magazine, writer Javier Grillo-Marxuach says, "The Dharma Initiative was a communal research facility on the island. A lot of scientists and free-thinkers got together to do a lot of different kinds of research: psychiatry, zoology - and remember that with the zoology part of the film you saw some polar bears. It's possible there were some animal aggression studies going on there, as well as human psychology experiments and a whole variety of other things."
It turns out that Ben was a member of Dharma when he traveled to the island with his father when he was a boy. As a young adult, Ben helped ensure the demise of Dharma, killing most of the members. (Ep: 3x20, The Man Behind the Curtain)
The Dharma Initiative built several Dharma stations around the island.
Charlotte remembers and tells Daniel that she's been on the island before. She grew up there and they were part of The Dharma Initiative, until her mom made them leave without her dad (Ep: 5x5, This Place is Death).
Sawyer, Juliet, Jin, Daniel, and Miles go back in time to the Dharma Initiative days (Ep: 5x8, LaFleur). Sawyer is the head of security and Jin, Daniel, and Miles work for him. Juliet is a mechanic. Horace seems to be the boss over the initiative.
In 1977 Jack begins work as a workman, Kate as a mechanic, and Hurley as a chef (Ep: 5x9, Namaste).
