Here's what Wikipedia says for h:
In almost all dialects of English, the name for the letter is pronounced /ˈeɪtʃ/ and spelled ‹aitch›1 or occasionally ‹eitch›. The pronunciation /ˈheɪtʃ/ and hence a spelling of ‹haitch› is often considered to be h-adding and hence nonstandard. It is, however, a feature of Hiberno-EnglishEnglish2 and other varieties of English, such as those of Malaysia, India and Singapore. In Northern Ireland it is a shibboleth as Protestant schools teach aitch and Catholics haitch. In Australia, this has also been attributed to Catholic school teaching and is estimated to be in use by 60% of the population. The perceived name of the letter affects the choice of indefinite article before initialisms beginning with H: for example "an HTML page" or "a HTML page". The pronunciation /ˈheɪtʃ/ may be a hypercorrection formed by analogy with the names of the other letters of the alphabet, most of which include the sound they represent.
The non-standard haitch pronunciation of h has spread in England, being used by approximately 24% of English people born since 1982 and polls continue to show this pronunciation becoming more common among younger native speakers. Despite this increasing number, careful speakers of English continue to pronounce aitch in the standard way, as the non-standard pronunciation is still perceived as uneducated, at least in most of the United Kingdom. The pronunciation haitch followed the introduction of Phonics and was designed to help prevent working class children from dropping the initial H in words such as hospital (otherwise pronounced as 'ospital).
Authorities disagree about the history of the letter's name. The Oxford English Dictionary says the original name of the letter was [ˈaha]; this became [ˈaka] in Latin, passed into English via Old French [ˈatʃ], and by Middle English was pronounced [ˈaːtʃ]. The American Heritage Dictionary of the English Language derives it from French hache from Latin haca or hic.
Then of course there's the "zee" (USA) vs. "zed" (rest of the English-speaking world?) pronunciation for ZZ; apparently we Americans can thank Noah Webster for that one.