Most D20s I own (with the exception of poorly made foam ones or MTG spin-down dice) seem to have all opposing sides add up to 21 (20 + 1, 15 + 6, etc). Why is this? Who started this?
Opposite sides add up to 21 on a d20 for the same reason that opposite sides add up to 7 on a d6: if there's a manufacturing or design defect, and the die ends up slightly flatter than intended, then the average result of the die will not change.
Consider a d6 that ends up a bit flat: two sides opposite each other will both have an increased chance of being landed on. But since these two sides' numbers are "opposite" to each other, they will not affect the average of the die. For example, a d6 might have a 1/3 chance of landing on a 1, a 1/3 chance of landing on a 6, and, and a 1/12 chance of landing on each of the other faces. The average of this seriously-deformed die is: 1 * 1/3 + 2 * 1/12 + 3 * 1/12 + 4 * 1/12 + 5 * 1/12 + 6 * 1/3 = 3.5, the same as a normal die.
Of course, various other deformities (malformed corner, air bubble in the plastic, some enterprising fellow put a little lead in the die, etc.) will still play merry hob with the probabilities in an unfair way, but a flattened die will be somewhat fair in that its biases favor both high and low numbers equally. The layout for d8, d10, d12, and d20 dice were probably created from this same idea to make the dice somewhat fair if they're flattened.
I may be misinformed, however my understanding of the situation is that this is a result of trying to normalize the value of each region on the d20.
The best comparison is between an MTG spindown (where the numbers count down from 20-1 in sequence spiraling around the d20) and a regular d20. A spindown has all the high values clustered at one end, and the low values clustered at the other. with practice, you could easily learn to roll a spindown to get 10 or more the vast majority of the time, for a regular d20 this is impossible as the numbers are spread evenly, so high numbers are surrounded by lower numbers.
It is very hard (if not impossible) to roll a d20 for an exact individual side, so spacing them out in this way is the best way to "balance" the values, such that a practiced roll aiming for 20 has a high chance to land on much lower numbers that are adjacent, where a spindown would have other high numbers adjacent.
by laying out the numbers such that all sides add up to 21, you give a memorable way for users to navigate a d20, whilst also giving a reasonable (if not optimal) proportionality in value accross the areas of the d20.
as for who started it, I couldnt answer that, d20 themselves have been around since the Romans (http://www.wired.com/geekdad/2008/06/what-version-of/), but I can find no information on who decided the numbering scheme.