Cosmetics are very complex products (lots of different substances) and it is quite hard to really understand if one product is 100% vegan or not.
This article touches the surface of some non-vegan substances that are used for cosmetics:
- Lanolin as emollient
- Shellac in nail or hair products
- Glycerine is used for a broad range of products that include soaps, hair care, make-up, and moisturizers
- Casein in hair or face treatments products
- Guanine for providing spark for various products such as nail polish, eyeshadow etc.
- Oleic acid for a moisturizing effect
- Stearic Acid
- Carmine for the natural red color
- Collagen promoted as having an anti-aging effect
As a side note, I also recommend reading this article which provides a great insight into the chemistry of cosmetics. Besides the rather complex chemical cocktail of many cosmetics, what is worse is that not all ingredients are put on the label:
Chemicals, both natural and synthetic, are added to cosmetics to
provide an appealing fragrance. Even ‘unscented’ products may contain
masking fragrances to mask the smell of other chemicals.
The term ‘fragrance’ is often a generic term used by manufacturers. A
single listing of fragrance on your product’s ingredient list could
represent dozens or even hundreds of unlisted chemical compounds that
were used to create the final individual fragrance.
Manufacturers do not have to list these individual ingredients as
fragrance is considered to be a trade secret.