Vegetarians don't eat...
Gelatine
Made from animal ligaments, tendons, skin and bones!
Often found in sweets (including marshmallows), biscuits, margarine, yoghurt, mousse, medicine capsules, vitamin / mineral supplements and some coloured drinks. Sometimes found in chewy sweets, cakes and biscuits. Fortunately vegetarian alternatives to gelatine medicine capsules are becoming more widely available.
Fish
Vegetarians definitely do not eat fish!

For further information see the Vegetarian Society's Fish Campaign.
Rennet
An enzyme traditionally sourced from the stomach of slaughtered, newly-born calves and used to make cheese.
Vegatarian cheeses are manufactured using rennet from non-animal sources. Many UK cheese manufacturers use vegetarian rennet, so look out for those packs marked "suitable for vegetarians".
Whey and whey powder are usually by-products of making cheese. Vegetarian whey is a by-product of making veggie cheese. Unfortunately, because it is possible to buy non-vegetarian cheese it is also possible to find whey that is not suitable for vegetarians. Look out for the VegSocApproved symbol to ensure that any products that include whey are suitable for veggies.
Animal fats
Made from the tissues and bones of slaughtered animals and sometimes used in the manufacture of margarines, cakes, pastries and biscuits. Lard and non-vegetarian suet are types of animal fat.
Cochineal
A red colouring made from crushed insects! Also known as E120 and sometimes called Carmine, it is used as a food and drink colouring and can be found in some biscuits, desserts, coloured drinks and sweets.
Battery farmed eggs
Many vegetarians will only eat free-range eggs because of objections to the animal welfare issues involved in the battery farming of hens. The Vegetarian Society only approves products containing eggs if they are free-range.
For more information on battery farmed hens.
For more information on vegetarian stumbling blocks.