Palm OilPalm oil, along with olive and coconut, is one of the top oils used by soap makers today. Because of the qualities it gives soap, it is often called "veggie tallow" in that it gives many of the same qualities that beef tallow does - a hard bar with a rich creamy lather. Alone, it's pretty unremarkable, but combined with other oils like olive, coconut and castor, it makes great, hard, long lasting soap. There are some serious concerns about palm oil farming in Malaysia - and the impact it is having on both the land and the people. For more information on the palm oil controversy, see Costly Oil Means Costly Calories - The Controversy Over Palm Oil. I know several soap makers who have eliminated palm oil from their recipes because of this.
Palm Kernel OilThough it comes from the same plant/nut as palm oil does, palm kernel oil is almost identical in its soap making properties to coconut oil - giving a nice hard white bar of soap...with lots of luscious lather. Palm kernel oil is often available partially hydrogenated, in easy to handle/measure flakes...or just as a standard liquid oil. As with coconut, you can use it up to about 30% or 35% in your recipes. However, like palm oil, palm kernel oil is surrounded by the same environmental and human concerns. See Costly Oil Means Costly Calories - The Controversy Over Palm Oil
Pumpkin seed oil is a rich and vitamin-filled oil with abundant antioxidant properties. It contains Omega-3 and Omega-6 fatty acids, as well as vitamins A, C, E, and Zinc. It's fatty acid balance is most similar to soybean and sunflower oil, and will contribute about the same qualities to soap that they do in terms of hardness, lather and conditioning. Most soap makers I know save the super-premium nourishing oils like pumpkin seed for special skin care products, and focus on the more basic oils for soap making. That said, in terms of pure marketing appeal, it's a wonderful luxury oil to add (a bit) to a batch of pumpkin soap.
Rice Bran OilA few years ago, there was a spike in the price of olive oil. Soap makers across the country scrambled to find more affordable alternatives for their soap. Rice bran oil came to the rescue. Expressed from the husks of rice, most soap makers found that rice bran oil imparted nearly the same creamy, moisturizing qualities that olive oil did to their soaps, but at a lower price. It does have a lot of the same antioxidants and vitamins that olive has, and a similar fatty acid make up. I like it in both bar and liquid soaps. The only disadvantage of rice bran oil is its short shelf life - (6 months or so.)
Safflower OilIts fairly short shelf life, and fairly unremarkable fatty acid makeup, have made safflower oil pretty neglected in soap making recipes. If you have it on hand, you can certainly use it in your recipes like you would soybean, canola or sunflower - at 5-15% or so. In soap, it is mild and moisturizing.
Sesame Seed OilLike neem oil, sesame oil has a characteristic scent that must be dealt with if used in a high percentage in your soap. In your soap recipes, sesame oil will be moisturizing and conditioning. It is high in antioxidants and vitamins, so it's also nice in lotions, balms, massage bars and massage oils.
Shea OilShea oil, or liquid shea, is fractionated shea butter, one of the most popular luxury oils used in soap making recipes. This variation of shea butter is liquid at room temperature and wonderful for adding to melt and pour soap, massage bars, or to creams and lotions. I've also used it in bath bombs. It's very moisturizing in the tub, but may be a bit too oily for some folks. But the fact that it's liquid doesn't give any benefits in soap. So if you're going to use shea butter in soap, go ahead and use the actual shea butter instead of liquid shea oil.
Soybean Oil, LiquidSoybean oil, like canola, safflower and sunflower, is often used as a portion of a soap making recipe in combination with other "core" oils like coconut, olive and palm. It's pretty unremarkable, but if you have it on hand, use it 5-15% of your soap recipe. It is mild, moisturizing and gives a low, creamy lather. Because soybean oil is so readily available and economical, many cost-conscious soap makers will use soybean as a part of their soap recipes to reduce the overall cost of their soap batches.
Soybean Oil Shortening
Soybean oil, in its hydrogenated form is generally called vegetable shortening & sold under generic names, or the brand Crisco. Shortening is usually a blend of soybean & cottonseed oil, and makes nice soap. Like all soap making oils, except olive, it's not a great oil to use alone, but combining it with olive & coconut makes a good, stable, bubbly, moisturizing bar of soap.
All of the soap recipes in Sandy Maine's book, "The Soap Book" are made with 44% vegetable shortening (Crisco), 28% coconut and 28% olive oil. If it's good enough for Sandy Maine (of SunFeather Natural Soap Company), it must be pretty good. (Note: Her book was published before the controversy over cottonseed oil arose though. (See above.) She may have reconsidered.)