Source: Hidden Animal Ingredients in Foods (dummies.com), slightly modified and extended.
Can be vegan, or animal based:
Glucose (dextrose) - Animal tissues and fluids (some glucose can come from fruits)
Glycerides (mono-, di-, and triglycerides) - Glycerol from animal fats or plants
Lactic acid - An acid formed by bacteria acting on sugar, often lactose.
Lecithin - Phospholipids from animal tissues, plants, and egg yolks
Oleic acid (oleinic acid) - Animal tallow
Rennin, rennet - Produced by microbes, or extracted from calves stomachs.
Stearic acid (octadecanoic acid) - Tallow, other animal fats and oils. Sometimes made from cocoa butter or shea butter.
Vegetarian, but not vegan:
Albumin - The protein component of egg whites
Casein (caseinate) - A milk protein
Lactose (saccharum lactin, D-lactose) - Milk sugar
Lutein - Deep yellow coloring from marigolds or egg yolks
Whey - Watery liquid that separates from the solids in
cheese-making
Neither Vegan Nor Vegetarian:
Carmine (carmine cochineal or carminic acid) - Red coloring made from a ground-up insect
Fish Sauce - Common ingredient in Thai cooking that is almost never listed on the menu
Gelatin - Protein from bones, cartilage, tendons, and skin of
animals
(sometimes gelatin is vegetarian and made from artificial ingredients)
Isinglass - Gelatin from the air bladder of sturgeon and other freshwater fish
(Often used to filter Alcoholic beverages)
Pepsin - Enzyme from pigs’ stomachs
Suet - Hard white fat around kidneys and loins of animals
Tallow - Solid fat of sheep and cattle separated from the membranous
tissues