The Apostrophe

The apostrophe referred to here is a punctuation mark in written English. It originated as a mark to show that something was missing. Confusion arises because one of these omissions, that of the letter "e" from the genitive -es ending in Old English, is now more likely to be described as "possession" (belonging to). So though there is a single origin there now seem to be two roles for the apostrophe.
The rules governing the use of apostrophes in written English are basically very simple.

Essentially there are two uses:

1. Omission.
They are used to denote a missing letter or letters, for example:
I can't instead of I cannot
I don't instead of I do not
it's instead of it is

2. Possession.
They are used to denote possession, for example:
the dog's bone (the bone belonging to the dog)
the boy's book (the book belonging to the boy)
- And if there are two or more dogs, boys etc, the apostrophe comes after the 's':
the dogs' bones (the bones belonging to the dogs)
the boys' books (the books belonging to the boys)

Four additional notes:
A. The possessive form of 'it' does not take an apostrophe. So do use the apostrophe 'its' when you mean "it is" but use "its" (no apostrophe) for "belonging to it".
B. Do not use an apostrophe for the possessive pronouns eg ours, yours, his or hers
C. In the phrase "the dogs' bones" it is the number of dogs that is important, not the number of bones! So "the dog's bones" means the bones of one dog with several bones; "the dogs' bones" means several dogs with several bones.
D. Although commonly seen, it is not correct to use an apostrophe after an acronym. So CDs and DVDs but not CD's and DVD's
So the two simple uses become slightly qualified, which muddies the waters.

A Social Issue
Furthermore, as in some circles correct use of the apostrophe is taken as a measure of literacy - or even intelligence - its use has come to be a disproportionate irritation for both teachers and students.
Also it has become a social issue, with errors placed on public display to be scoffed at smugly by those who can use it properly.

The supporting argument is usually that the apostrophe gives us extra information (how many boys, how many dogs) which is important to us. In speech we usually have more context, while intonation and gesture help us fill in any linguistic gaps. In writing we have less information and punctuation seeks to tell us about pauses and to calify sentence structure. However it is quite rare for confusion in meaning to arise from a missing apostrophe. Ambiguity is more likely when an apostrophe is used in the wrong place rather than not at all. And note how the examples of incorrect usage are identified. If they are so obviously wrong, does that not suggest that the meaning was clear in the first place and therefore the apostrophe was redundant?

The present author experienced the frustration of unsuccessfully teaching use of the apostrophe to hundreds of pupils and feels the time has come to abandon it entirely. Already large signs (City Drops Apostrophes!) and shop names have abandoned this irritating little mark. Contrived examples such as Fo'c'sle are largely redundant and there is a strong case for saying that we would not miss it if it disappeared.

By not using it at all perhaps we could actually increase clarity and remove one small source of annoyance for teachers of English.