A language structure, typical of English and other languages of Germanic derivation. It indicates ownership and it is formed, in its simplest case, by adding an apostrophe and an S to the word that indicates the owner.

Don't confuse with the similar looking but vastly different contraction of is into 's. So, the room's over there is not a Saxon genitive! It is just the third person singular of the verb to be.

my uncle's cat has exploded
John's wife is a beautiful woman
Mary's husband's job pays well

The third example is two genitives in sequence, a case that is not so common but is nonetheless possible. Genitive is the case of possession, and in the original form it was indicated by an -es suffix as in Chaucer's titles: The Clerkes Tale, The Milleres Tale. If the name already ends in S, as is the case with most plurals, an apostrophe is simply added at the end of the word: the Italians' love for their mothers, Charles' house (but also, Charles's house).

One difficulty for learners of English is determining the appropriateness of using the saxon genitive. One easy rule of thumb is that the owner must be an animate being. Thus

I speak the Queen's English!
A cat's whiskers should never be trimmed

While the *stone's colors range from red to brown would be not acceptable for most speakers. It is also quite OK to form the genitive with associations of animate beings, like herd, audience, gang. Then it seems that there is a vast amount of special cases. Some of them are:

  • expressions of time, like seasons (last winter's snows)
  • abstract expressions related to thought and ingenuity (the project's scope was impressive).
  • natural phenomena (the earth's rotation but not *the earth's satellite photograph)

Additionally, it seems that to some speakers choosing a Saxon genitive connotes informality; contrast Milton's poems with the poems of Milton.
And of course, there is a raft of idiomatic expressions; to get your money's worth, at arm's length, and your heart's desire.

William Safire type would also observe that there is growing confusion between the saxon genitive, the plural form and certain contractions. A typical case is the its/it's imbroglio in which the 's is not a saxon genitive but a contraction of is. There is also a disturbing passion for marking certain plurals of foreign words ending in a vowel with apostrophe-s; *These pomelo's are delicious.

liveforever says:the saxon genitive has begun to infect Danish (where the genitive -s carries no apostrophe) to the extent that using apostrophic S in genitive is now the most common Danish grammatical error. (*sigh*)

Ultimately, the correct usage of the Saxon genitive is a fuzzy concept, with US speakers typically using it more widely, and UK speakers more restrictively. Even Gritchka declare that they feel little restriction when using this form.

Traditionally in linguistics the * indicates expressions that are not acceptable. Many thanks to liveforever, Cletus the Foetus, Gritchka and the other noders that wanted to comment on this.