A Brief History
To begin at the beginning, as they say in all the best yarns, one should go back to 1938 in Kuala Lumpur in what is now Malaysia when a group of ex-patriates associated with the rubber plantations started a modified paper chase in order to work up a decent thirst before retiring to the Selangor Club. There the restaurant was known locally as the "Hash House" so naturally the name was adopted by the harriers and in contrast to other groups undertaking similar activities the name stuck. The particular genius of the founding father, A S Gispert, nicknamed "G", was to make the traditional hare & hounds running more fun by making it non-competitive. But you knew all that really, didn't you?

So we will move on quickly to the Second World War and its aftermath which became known as the Malayan Emergency when British and Australian troops joined in the fun and when posted elsewhere began new chapters and the Hash House Harriers spread throughout the world rather like the AIDS virus spread from a central origin in Africa. You knew that, too? Well, perhaps not the fact that Hashing is an affliction akin to AIDS but how's this for exponential growth:

Date       Event
1938       Kuala Lumpur H3 (Mother Hash) founded
1947 Royal Bordighera H3 founded - first known offshoot, ceased early 1960s
1962   Singapore H3 founded
1967   Dhekelia H3 - second hash in Europe, after RBH3 above.
1967   Sydney H3 - first Hash in Australia
1971   Fort Eustis H3 - first Hash in the North America
1969   Commando Forces H3 founded - first Hash in UK
1971   Westcombe Park H3 founded - oldest monthly running Hash in UK
1973   KL H3 1500th run - 35 other Hashes "known" to exist
1974   Bicester H3 founded - oldest weekly running Hash in UK
1975   Surrey H3 founded
1976   London H3 founded
1977   90 Hashes known in 35 countries
1984   Harrier International founded
1986   555 Hashes known in 85 countries
1988   700 Hashes known in 125 countries
2000   1570 Active Hashes known in 184 countries with 200,000 hashers

Both servicemen and diplomats have been largely responsible for the contagion spreading and indeed the first known recorded hash in the UK was the Commando Forces H3 based at Plymouth founded in 1969 by the then Col Ray Thornton (ex-JM of Singapore H3) which flourished in the early seventies but like many military hashes petered out when postings decimated the membership Ray went on to found Bicester, Donnington and Looe & Liskeard which survived by becoming predominantly civilian hashes.

See also the entry in Wikipedia on hashing.

Note: Tumbling Bill of Kuala Lumpur H3 is maintaining a family tree of all the hashes in the world founded since 1938