Please feel free to contribute and add to (or correct) anything here. Some of you are professionals and/or have been to culinary school and will have a much better grasp on this than I do.
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For the following types of flour, I mention the protein content. Why? The amount of protein in flour is important in flour mixes as, when they come into contact with moisture, they release the gluten that gives your baked goods strength, shape and elasticity. The flour you choose will affect the final product, as will substituting the wrong type of flour into a recipe. Higher protein gives a stronger or denser product, lower protein gives softer, more crumbly texture. High protein flour in cake or pastries will result in a dense and chewy product, where using a low protein flour for bread will result in a soft texture with a cakey crumb.
- Plain: Plain flour is synonymous with all-purpose flour. It contains no leavening agent and typically has 10-12% protein, though this will vary across brands, seasons and regions. It's often made from a blend of different types of wheat and is designed to have a decent result across a large variety of different products. It can be used effectively in most baked goods, particularly cakes, cookies, pastries and breads.
- Self-Raising Flour: Also known as self-rising flour or, uncommonly, phosphated flour. It is simply plain flour that has had a leavening agent and a little salt added to it. You can taste the salt in the flour, which is a good trick to remember if you forget to label your flours and can't tell if it's plain or self-raising. Its main advantage is that you don't have to add the leavening agent yourself, though some people caution against this as you cannot guarantee that the leavening agent is equally dispersed throughout your flour (it won't make a phenomenal difference and most home bakers won't care). Like plain flour, it's designed to be useful across the board. If you don't have any on hand, or can't get it, mix two teaspoons of baking powder per cup of plain flour, or use one teaspoon of cream of tartar and half a teaspoon of bicarbonate per cup of plain flour.
- Cake Flour: Cake flour is made from soft wheat flour, with a high starch content and a lower protein content (typically 6-8%). Cake flour isn't just for cakes: it's desirable whenever a more delicate texture is required. It's often used in cookies, muffins, biscuits, pie crusts and cookies. During baking, the proteins set faster and don't spread as much, and the fats become more evenly distributed (resulting in a better texture). Recipes with a high sugar-to-flour ratio are best suited to cake flour as they will rise better and be less likely to collapse. Here in Australia, the wheat is a lot harder, so cake flour is fairly rare to come across (in fact, I've never seen it. I assume some store somewhere would import it) so I always have to make it myself. If you can't find cake flour, it's easy enough to make by replacing two tablespoons of flour per cup of flour with cornflour (corn starch), or use a ratio of 3 parts plain flour : 1 part cornflour.
- Bread Flour: Also known as bakers flour, bread flour has the highest protein content of all flours (typically 12-14%). It will require more kneading to properly develop the available gluten. It's great in recipes that use yeast, or where strength is required (e.g. choux pastry and puff pastry). It's the best choice for yeast breads as the gluten creates a network with enough strength to trap the gases from the yeast. If you don't have any or can't get it, the best substitute is plain flour: try to get one on the higher end of the protein spectrum. The rise won't be as good with plain flour, but it will still be decent.
- Pastry Flour: Sometimes called cookie flour, pastry flour has a high starch content and low protein content. It is similar to cake flour, but it has not been chlorinated and as such is a little harder (around 8-10% protein). It's uncommon, usually found in health or speciality stores. As the name suggests, it's great for pastries as well as pies and cookies as the final product is tender and crumbly. To make your own by mixing a ratio of 2 parts cake flour to 1 part plain flour (though I have read some people use a 1:1 ratio and others 3:1 -- personal preference and experience will influence your choice).
- Whole Wheat Flour: Also called whole meal flour or graham flour. As the name suggests, it is produced from the whole wheat kernel. It is darker in colour, grainy, and high in dietary fiber (and higher in overall nutrients). While it is high in protein, it's not very good at forming gluten. For that reason, it is often blended with plain flour or bread flour to increase the elasticity. Whole wheat flour will go rancid more readily that other flours. It has a shelf life of a few months if stored in the pantry so it is often better to keep it in an air-tight container in the fridge. The protein content will depend on the type of wheat used. Soft white whole wheat sits around 9-11%, where red or golden wheat is around 15-16%.