But most of these changes took place organically - that is to say, there was no central committee whose job it was to regulate the alphabet, introducing and phasing out words deemed either redundant or required; for example, Etruscan had no /g/ sound, so they made Greek's gamma (Phoenician's gaml) a <c>, and used it as one of their /k/ sounds (in addition to <k> and <q>). There may be some exceptions: for example, there is a story related in Plutarch that Spurius Carvilius Ruga (or, as spelled in Greek, displaying some differences in orthography, Σπόριος Καρβίλιος) added a stroke to the letter C in order to accommodate the /g/ sound in his name, since the Etruscans had done away with the gamma. If true, this story represents one example of top-down alphabet change. By contrast, the letter <z> was rntroduced by no-one in particular, after the Romans decided they could no longer transliterate the pesky zeta with <s> or <ss>. Even though the letter was officially removed in the first place by the Censor Appius Claudius Caecus (as in the Appian Way) around 300BC, after rhotacism made it defunct (or he didn't like the face people pulled when they said it, cf. De Nuptiis Philologiae et Mercurii, III.261).
But there are also examples of attempts to add to the alphabet falling flat: the Emperor Claudius tried to add three letters to the alphabet, and was so monumentally unsuccessful that today scholars don't even know what one of them was. One was a "(reversed, upside-down digamma), which stood for the semivowel /w/"; the other, a plus sign without a west-pointing arm (if you see what I mean) "was used in place of the letter ypsilon in Greek names. Its phonological value is unclear. A third letter, which is reported to have stood for the cluster /ps/, has not yet been found in an inscription. Its precise form is uncertain; the Latin grammarians cite several possibilities."*
There have been attempts more recently to effect "alphabetic reform" on the English language, and not just lame April Fool's jokes or slightly less lame YouTube sketches (I actually found it quite funny) - or indeed nutters on Yahoo! Answers. Most notably, Benjamin Franklin tried in 1768 "to give the alphabet a more natural order":
This is quite succinctly summarised and illustrated here. More recently, also in America, was the publication in 1905 of "A Plea for Alphabetic Reform" by Benn Pitman. Notwithstanding his inability to spell the word "Pharaoh" (see p.4), he did pioneer shorthand writing (or phonography). Interestingly, his New York Times obituary from December 29, 1910, reports as follows, and you may make of it what you will:
Beyond that, there is the interrobang, which ended with a whimper, and which wouldn't even really have become part of the alphabet, unless one classed it with the ampersand ("&"), so named because students rattling off their A-Z would add at the end, "and, per se, 'and'". In that sense, the ampersand was considered to some extent a 27th letter (or at least, that's what Wikipedia says).
By the way, if anyone knows anything about James Joyce and Finnegans Wake (I certainly don't), they might be able to connect this to the "abcedminded" and "allaphbed" puns that are found there? And "letters" and "lettrines"?
* A Companion to the Latin Language edited by James Clackson, who, by the way, can be heard voicing-over this brilliant clip (<3 BBC).