Painting by Willem deKooning.
DeKooning experimented with safflour oil, Pollock used a gloss enamel synthetic paint. For centuries, the quest to find a perfect fluid consistency of paint that is also reliable has been pursued by artists. When oils such as walnut, linseed and poppy seed were added to pigments around 1300, they replaced egg tempera as a binder. Oil paint produced smoother brushstrokes and paint that would stay workable for long periods of time.
Some artists like to use thin paint when starting a painting, so here are a few rules. In most cases, linseed oil mixed with paint is sufficient. It is not recommended to thin paint with turpentine (or Gambosol), as they will eventually separate from each other. A rule of thumb is not to exceed 20% of the blending media when mixing with oil paints, as it will fare better over time. Some mediums create a glossy finish. If a gloss is not desired, a varnish can be applied after the painting is completed.
Recipes beyond linseed oil:
Keith at Colsnow Art Supplies likes:
Oil of Spiked Lavender
Venice of Turpentine
David Titterington likes:
Morager for wax-like effects achieved by artists such as Rembrandt.
Morager has many recipes, but is generally made with white lead paint and boiled linseed oil
David gets his from here: http://www.fallikstudio.com/medium.htm
Some artists prefer the smell of walnut oil.