Other ingredients
Apart from grain, water, hops and yeast there are hundreds of other ingredients that can go into beer. Some of these additives are traditionally used in beer, while others have only begun to be used recently as microbrewers push the boundaries of brewing. These ingredients, along with unmalted grains, are not essential ingredients in beer and are referred to as adjuncts.
Sugars
One of the first things that new homebrewers are told is to not use table sugar, or sucrose, in their beers because it gives them a "cidery" taste that some people call a "homebrew tang". While it's generally true that brewers should avoid using sucrose, there are some recipes that call for small quantities of cane sugar or beet sugar to change flavour or colour of a brew, or increase its alcohol content without adding to the body. Table sugar such as demerara, brown sugar and raw sugar fall into the category of sucrose but are sometimes used in beers, again in small quantities.
Invert sugar is cane sugar that has already had some of its molecular bonds broken, which makes the yeast's work easier. Because the yeast does not have to make the invertase enzyme to break down the molecules, it is widely accepted that invert sugar does not produce cidery “tang” associated with regular cane sugar.
Dextrose and glucose are totally fermentable and so add alcohol but no taste or body to your beer, and are often used by homebrewers in place of sucrose. Most experienced homebrewers will not use these adjuncts, however, because it is easy to make a beer without them and it's not an ingredients used in most commercial beers.
Belgian candi sugar adds a smooth taste, body and alcohol without being very apparent. It is available in different colours, influencing the appearance of a beer. Darker candi sugar may add a rummy character to stronger Belgian styles.
Lactose, or milk sugar, is not fermentable so makes beer sweeter. It is used to make milk stouts and sweet stouts. However, compared with cane sugar it is not very sweet so needs to be added in relatively large quantities to have much of an effect. As a start, use at least 250 grams in a 23-litre brew. It's easy to add more lactose next time you brew the beer, but not so easy to remove it if you overdo it the first time!
Maple syrup, when used in small amounts, adds a dry, woodsy, smoky flavor. Larger amounts can be strongly sweet.
Honey, molasses and golden syrup are all highly fermentable and can be added to beer to produce specific tastes and styles. Honey needs to be used in quite large quantities (more than 500 grams in 23 litres) to be noticable, whereas golden syrup or molasses should be used sparingly as it can overpower a beer.
Herbs and spices
Hops haven't always been used to flavour, bitter or preserve beer. In ancient times, various herbs were used in beer and it's only relatively recently that hops have been the main bittering agent.
Even once hops became an accepted ingredient in beer, various herbs and spices were used alongside them. For example, ground coriander seed and dried orange peel have been added to some Belgian wheat beers, or witbiers, for years. In more recent times, brewers of American spiced pumpkin beers, which are brewed around halloween, add spices such as cinnamon, allspice, vanilla, nutmeg, mace, cloves and ginger, along with pumpkin. Chilli is another spice often seen in beer, from light lagers to dark stouts.
When it comes to adding spices and herbs to beer, it's about what works. Many have tried and liked the spices mentioned above. Others have added spices such as star anise. If you want to add spices or herbs to your beers, start with very small quantities because it's a lot easier to add more next time than it is to remove some from your current brew if you go overboard. Remember that the herbs and/or spices are there to complement the beer, not dominate it. Don't overdo it.
Fruits and vegetables
Cherry, peach, apricot and raspberry are just a few of the fruits that are added to beers. You may also find beer with mango or a bit of grape juice in them. Pumpkin, found in American pumpkin ales, along with various herbs and spices, is probably the most widely used vegetable in beer. As with herbs and spices, the fruit or vegetable should complement the beer, not overpower it.
Head improver
If you find you are getting bad head on your beer, you may be advised to add vegetable starches such as corn syrup, dried corn syrup or malto-dextrin to improve things. Before you do this though, consider that a bad head may also be caused by dirty glasses (have you rinsed them thoroughly in hot water after washing to remove all traces of detergent?). Identical glasses can also produce different heads. If you're having trouble, try sratching a cross in the bottom of the glass with a glass cutter. A fantastic head can be had without any "head improver" and using such adjuncts is frowned upon by most brewers and considered unnecessary.
Many brewers add unmalted wheat to their beer to help with head retention.
Fermentation modifiers
These are enzymes that allow yeast to consume sugars it would not normally be able to, resulting in a beer with a slightly higher alcohol content, thinner body and fewer carbohydrates in the form of sugar. The enzyme is added at the same time the yeast is pitched.
Most homebrewers do not use fermentation modifiers, as there are other ways to achieve the same result. Kit brewers can substitute some less-fermentable sugars such as malt extract for more fermentable sugar such as glucose of dextrose.
For all-grain brewers, mashing at a slightly lower temperature will produce more fermentable sugars and fewer unfermentable sugars, resulting in a drier beer with less body.