... with examples from House
mirankos asks: "What is incorrect about saying 'keep this between the three of us'?"
Look carefully at the word "between" and you will see the letters "tw" together, just as in the word "two." That's no accident!
The word "between" comes from an Old English root meaning "two," and its most basic meaning is spatial, referring to an object positioned with one each of two other objects on each side - in other words, to an object between two other objects.
If you're dealing with more than two objects, you use the word "among" instead. Thus, if House is talking with Wilson, he might say, "Well, actually, I think Cuddy was right this time, but let's keep this between the two of us." On the other hand, if he's talking with Wilson and Cuddy, he's much more likely to say, "There's only one set of bodacious gazongas among the three of us!" Or, for an even larger group, House might say, "I have to choose only three from among the candidates trying to get those fellowship positions."
Sometimes, although you are talking about a larger group of people, you are thinking specifically about one-to-one relationships within that group. Among tends to have a rather vague, collective connotation, and it really wouldn't work for that situation. Thus, you would go ahead and use between: "There are some intense personal rivalries between the doctors vying for House's fellowship openings."
The word "betwixt," by the way, comes from the same root and has the same meaning. It is now considered archaic and is usually found only in literary or poetic uses. You will sometimes still see it used in the phrase "betwixt and between."
If it helps you to remember, you may wish to think of the word "twain," which sounds more like "between" than plain old "two" does. "Twain" also means two. It survives in the expression, "never the twain shall meet," (from "The Ballad of East and West" by Rudyard Kipling) and in the nautical measurement, "by the mark, twain," (i.e., the water is two fathoms deep), from which a popular 19th-century American author took his pseudonym.
One thing that can make it difficult to remember the different meanings of "between" and "among" is that the distinction isn't universal. Latin, for example, uses inter indiscriminately for "between" and "among." Following in their parent's footsteps, Spanish and French use entre for both meanings. Even the German word zwischen, which appears to be formed in a manner parallel to the English term "between" (zwei is German for two), is used to mean both "between" and "among."
On the other hand, Latin makes a similar distinction in a place where English doesn't, which winds up having an effect on another English vocabulary word. In Latin, the generic word for "other" is alius, from which English derives words like "alias." Latin also has another word, alter, that is used only when you're talking about the other of two. This comes into English as the root of the verb "alternate," whose basic meaning has to do with two objects or elements taking turns. For example, Chase and Cameron might alternate choosing where to go after work (i.e., Chase gets to choose today, and Cameron gets to choose tomorrow, then Chase gets to choose the day after tomorrow, etc.), or a patient might have alternating red and white stripes all down one arm (first a red stripe, then a white stripe, then a red stripe again, and so on), which means the most recent diagnosis was wrong and Amber is going to blame Thirteen. From this Latin term we also get an English noun, "alternative," which technically means another option when you only have two. Here's an odd bit of trivia with which you may impress your friends and intimidate your enemies: you're not supposed to have more than two alternatives. If you have more than two possible choices, you're looking at options, not alternatives, and you'll have to choose among them - not between them.
Resources:
The Oxford English Dictionary, Compact Edition
Langenscheidt's German-English English-German Dictionary
Langenscheidt's Pocket Spanish Dictionary
Larousse's French-English English-French Dictionary