Cornstarch, or cornflour to use the British term, is beloved in pies, puddings and gravies not just for its thickening ability, which is prodigious. It also keeps the sauce or pudding relatively clear or translucent. Nonetheless, there are a wide variety of thickeners available to you, and in many cases, they can be substituted freely. Learn how to use them, and you can throw off some of the shackles imposed by tyrannical recipe writers.
The beauty of cornstarch is that it is quite unobtrusive in a recipe and does not add a floury taste to foods. It imparts a glossy and translucent appearance. And it is a great thickener. One tablespoon of cornstarch will thicken 1-1/2 to 2 cups of liquid. It has it's drawbacks, though. Cornstarch thickens as soon as you add it to a hot mixture, so to keep it from forming lumps, it is generally mixed with a small amount of cool water or other liquid before being stirred into a hot mixture. Also, cornstarch looses some of its thickening ability if it is overheated.
Compared to cornstarch, white flour is an ugly stepsister. It has only half the thickening capacity of cornstarch. It does not leave your dishes looking shiny and translucent, but rather thick and dull. And it imparts quite a floury taste to your food. You really have to cook it into your sauce or pudding for several minutes to eliminate the raw taste. In many sauces, flour is mixed with butter to form a paste, which helps keep it from forming lumps when it comes in contact with the hot liquid. To use it in a pudding, you thoroughly mix one part flour with two parts of cold water before adding it to your pan. Ten tablespoons of flour in place of your five of cornstarch makes us think you'd be making more of a cake than a pie filling.
Arrowroot has many of the same qualities as cornstarch, and even a bit more thickening ability. It is also not as susceptible to losing strength if overheated. Its major drawback, though, is that it begins to lose its potency fairly quickly - often within one or two months. So you should buy it in small quantities and use it in place of cornstarch fairly often. Because it also thickens instantly, use it in the same way as cornstarch, by mixing it into a solution with cold water before adding it to the pan.
Tapioca flour is often used to thicken desserts, especially those that are intended to be cold, because it does not break down in freezing as flour-thickened sauces will. It is particularly susceptible to heat, though, and will become stringy when heated to boiling. One tablespoon of tapioca flour will thicken one cup of liquid. To thicken with tapioca flour, stir it into your mixture, bring it to a simmer, then remove it from the heat. Let it sit for 15 minutes - stirring only once or twice during the first five minutes - during which time, it will set.
Another thickener is potato starch. It behaves in much the same way as cornstarch, adding some translucency, thickening immediately, and breaking down in high heat. As with cornstarch, it is added to your mixture after being mixed in a solution with cold water. One tablespoon of potato starch will thicken a cup of liquid.
So recipe writers choose cornstarch because of its many positive qualities and because you only need half as much as you would of white flour, tapioca flour, and potato starch. Of the possible alternatives, only arrowroot equals or surpasses it. But, given its short shelf life, the arrowroot you have on hand is quite likely not going to work at full strength.