Here's a list of B vitamins, with their associated names, for my own reference (since I tend to forget these easily). The ones crossed out are no longer considered "true" vitamins. All the B vitamins are water-soluble. The common (accepted) ones are in bold.

"B" NameReal NamePurported PurposesVitamin B-1ThiamineB-1 helps the cells convert carbohydrates into energy. Supposedly also helps keep mosquitoes away, but this is apparently unconfirmed and most likely just urban myth. Is essential for the functioning of the heart and for healthy nerve cells, including those in the brain. Also helps the body cells convert carbohydrates into energy.Vitamin B-2RiboflavinBody growth and red blood cell production. Similar to thiamine, it helps in releasing energy from carbohydrates.Vitamin B-3NiacinNiacin is often prescribed by doctors to help reduce LDL (bad) cholesterol levels. Also helps maintain healthy skin and nerves. It is also important for the conversion of food to energy.Vitamin B-4Adenine???Vitamin B-5Pantothenic acidMetabolism of food, synthesis of hormones and cholesterol. Apparently helps clear up acne, as well.Vitamin B-6PyridoxineHelps the body use ingested protein, aids in the formation of red blood cells and in the maintenance of normal brain function. It also assists in the synthesizing of antibodies in the immune system.Vitamin B-7BiotinMetabolism of proteins and carbohydrates, synthesis of hormones and cholesterol.Vitamin B-8Ergadenylic acidRNA synthesis, as well as ADP and ATP synthesis. Helps break down food into energy and supports hormone functions.Vitamin B-9Folic acidSynthesis of DNA, production of red blood cells, and prevention of birth defects.Vitamin B-10Para-aminobenzoic acid (PABA)Protects the skin against ultra-violet radiation. Also helps with the breaking down of protein, and maintaining intestinal flora.Vitamin B-11Pteryl-hepta-glutamic acid???Vitamin B-12CyanocobalaminImportant for metabolism, formation of red blood cells, and maintenance of the central nervous system.Vitamin B-13Pyrimidinecarboxylic acid???Vitamin B-14Pterin phosphate???Vitamin B-15Pangamic acid???Vitamin B-16Dimethylgycine???Vitamin B-17Amygdalin???Vitamin B-18??????Vitamin B-19??????Vitamin B-20Carnitine????Vitamin B-21??????Vitamin B-22Aloe Vera extract????
Inositol and Choline Bitartrate are also related to the B vitamin family (inositol is sometimes dubbed vitamin Bm). Choline is good for enhancing memory and brain function. Inositol is used for the breakdown of fats and reducing blood cholesterol.

If you can help me fill in the missing information, please do share.