Rembrandt oil paints are my favorite because of their buttery nature. Simply highly concentrated pigment in linseed or safflower oil, they contain no fillers, no waxes, no fast drying agents. When we artists refer to the buttery nature of our paints we mean they are not stiff and hard to move. Rembrandt oil paints are buttery enough that I use no medium. Just mix directly from the tube.
Mediums like Liquin can give paint a smoother feel so it glides more easily. Another advantage is that the paint will dry more quickly. A disadvantage (and a major one I believe) is that you are diluting the color just as adding water to water-based paint dilutes the color.