It's a common misconception that baby oil is good for a baby's skin. Here's what Vimela McClure, founder of the International Association of Infant Massage, has to say about oils and infant massage:

For a number of reasons, I prefer cold-pressed fruit and/or vegetable oils to mass-produced, commercially advertised "baby oils." What we put on our skin is absorbed into the body and circulates throughout, carried by lymph, a liquid like blood that cleanses the body of toxins and carries away waste. If we are going to use a topical application on our little ones, we quite naturally want to use a product that will nourish them rather than one that may actually rob them of vital nutrients, being nonorganic and petroleum based. Most "baby oils" are primarily made of mineral oil. To make mineral oil, gasoline and kerosene are removed from crude petroleum by heating, in a method call functional distillation. By using sulfuric acid, applying absorbents, and washing with solvents and alkalis, hydrocarbons and other chemicals are then removed.

Not only is there no food value in this type of oil, but some nutritional authorities believe that mineral oil, when ingested, produces deficiencies of various vitamins, and they recommend against its use as a regular massage oil. When you are in the middle of the massage and your baby puts his hand in or near his mouth, you don't want to worry that a nonfood substance is passing into his delicate digestive system. Infants, whose brains and nervous systems are not fully developed, are particularly vulnerable to substances absorbed by the skin. Commercially produced mineral oils also dry the skin and clog its pores. Most modern pediatricians discourage their use for this reason alone. Theses oils were not made for regular massage, which encourages the absorption of whatever substance you are using. That substance, in my view, should be a food product that nourishes the skin.

Vimala McClure, Infant Massage: A Handbook for Loving Parents. Bantam Books, 2000. 64-65.

Oprah devoted a show to child and family safety, and included a segment on keeping your baby safe from baby oil.

I have found grape seed oil to be a readily available, natural and safe lubricant for infant massage.