Dictionary.com has a nice summary:
Don't is the standard contraction for do not. As a contraction for does not, don't first appeared in writing in the latter half of the 17th century, about the same time as the first written appearance of other contracted forms with not, like mayn't and can't. Don't remained the standard contraction for does not in both speech and writing through the 18th century. During the 19th century, under pressure from those who thought it illogical and who preferred doesn't in that use, don't for does not gradually became less frequent in writing but continued to be common in speech. Don't for does not still occurs in the informal speech and in the personal writing of many Americans, including the well educated, especially in the Midland and Southern dialects. It does not occur in edited writing or formal speech.
Don't started out as a contraction of "do not". The earliest examples of third singular + don't have this meaning, and are proper grammar because it's the subjunctive.
With the possible exception of the instance on line 1580 of The
Ordinary, all don’t’s stand for ’do not’. That instance no doubt also
stands for ’do not’, as it appears in a position where speakers of the
time would be likely to employ a subjunctive.
The Contractions of not: A Historical Note
I found an online version of The Ordinary (1751), and I think this is the instance on line 1580:
Pox o'your liquorous lips; if that she don't
After this sealing forty weeks deliver
Something unto thee as thy act and deed,
Say I can't Prophesie.
Use of the subjunctive has declined, and it is now "uncommon" or even "rare". According to Wikipedia:
The negated present subjunctive is always unambiguous with the third person singular (e.g., (that) he do not own).
According to the Dictionary.com quote, the first time don't was used as a contraction of doesn't was the late 17th century.
No matter for that; go, bid her dance no more, it don’t become her, it don’t become her, tell her I say so.
The Man of Mode (1676)
I am deceived if this Town don't teach her Wit.
But what pleases you don't please another; I like my own Way still.
The London Cuckolds (1682)
The paper The Contractions of not: A Historical Note (again) lists all these sources, saying:
This generalization seems likely to be related
to the decline of the use of the subjunctive where don’t with a third singular subject would have been natural.
I haven't found much in old grammar books (or similar) about this. The earliest source I found was English Language in Its Elements and Forms (1858), which says:
Don't is a contraction of do not, and not of does not. Don't for does not is a vulgarism.
It's certainly used outside of America, but the real question is how much? I'll give you some numbers for comparison.
In certain dialects of American English, spoken usage is really high. In particular, AAVE, as this quote says:
Note, finally, that don’t rather than doesn’t is the normal form in third person singular environments. Labov et al. (1968:247–248) find 83% (N = 90) use of don’t in NYC (96% among male teenage gang members), Fasold (1972:124) finds 87.5% (N = 24) use of don’t, and Weldon (1994:367) finds 86% (N = 94).
It also references some other American dialects:
Leveling to don’t is by no means restricted to African American English, since Wolfram & Christian (1975:116) found 85% in their West Virginia study, and Feagin (1979:198) reports 99% (N = 147) use of don’t among urban working class European Americans from Anniston, Alabama.
Negation in African American Vernacular
While not as high as in certain American dialects, there is still significant usage in British English:
The high presence of don't in the language of these speakers is in keeping with previous studies; thus, Anderwald (2002: 156) records an overall average for Britain of 30.1 per cent, this percentage increasing considerably in the case of the dialects of Central southwest England and Lower southwest England (52.1 per cent and 46 per cent respectively). To understand Anderwald's findings properly, we must bear in mind that they are based on BNC data, and that the demographic of this corpus includes speakers of all age groups, from young to elderly. By contrast, our data here are restricted to young speakers in London. Furthermore, Cheshire et al. (1999:78) also report auxiliary third-singular do as more frequent in the south than in the north.
He don't like football does he? A corpus-based study of third person singular don't in the language of British teenagers