“”You know, most people don't know the difference between apple cider and apple juice, but I do. Now here's a little trick to help you remember. If it's clear and yella', you've got juice there, fella! If it's tangy and brown, you're in cider town. Now, there's two exceptions and it gets kinda tricky here...
Cider is a beverage made by squeezing the juice out of apples and then fermenting it.
 The United States
In the USA it is commonly available either "soft" (unfermented) or less commonly "hard" (alcoholic). In its natural state it is an opaque, brownish-red, sweet-tart fruit juice; in this state it can be served as-is (it's a traditional fall drink in this form in much of North America, particularly associated with Halloween and Thanksgiving), spiced (aka "mulled"), or filtered and carbonated ("sparkling" -- a popular substitute for alcoholic beverages for children). "Apple juice" is not always clearly distinguished from soft cider, but is generally understood to mean a form of soft cider that has been clarified and rendered shelf-stable though pasteurization and/or concentration and reconstituting.
 The rest of the known universe
It is a fermented drink which is usually a pale golden liquid with about 5-6% alcohol by volume and a pronounced apple flavour, ranging from medium-sweet to bone-dry depending on the manufacturer and the market, and often carbonated. It can be further distilled into a type of brandy known as "applejack", the most famous type of which is the Norman French Calvados. A similar beverage, known as perry, is also made from pears.
Scrumpy is a variety of alcoholic cider made in the southwestern region of England. Glastonbury is a good place to start looking. The alcohol content of a good scrumpy is often much higher than that found in regular beer. English pubs, even those in the southwest, rarely serve scrumpy today because it allegedly turns even the nicest gentleman into a brawling brute. Those pubs that do serve scrumpy often serve a modified form that has been filtered, watered down and carbonated. If you are in the southwest looking for true scrumpy, seek out a local cider mill.
There is a part of Germany called Hesse where people drink an extremely sour 5-10% alcohol variant of cider (and pretty much nothing else), called "Ebbelwei" (apple wine) in the local dialect, a beverage that only starts to taste good after the seventh glass. That region (around Frankfurt) is the world's largest producer of cider.
Real alcoholic cider (US hard cider) lends itself to a few mixed drinks, including the Black Velvet (Guinness and cider layered in the manner of a black and tan) and the Snakebite (IPA or bitter mixed with cider). Non alcoholic (US soft cider) is generally drunk straight, but occasionally finds its way into some culinary uses, most notably cider donuts. Due to its reputation as a tipple of the poor, and possibly also because of the close association of the apple tree with northern European pagan religions, cider (and apples) were also a common scapegoat of 19th century Prohibitionists.