The canonical acrophony is an ideographic or pictographic writing system, where the letter's name and glyph both represent the same thing or concept - if e.g. the letter A in English, named "axe", were in the form of an axe.
The paradigm for acrophonic alphabets is the Late Bronze Age Proto-Canaanite alphabet in which the letter A, representing the sound /a/, is a pictogram representing an ox, and is called "ox" - ʾalp. The Latin alphabet is descended from the Proto-Canaanite, and the stylized head of an ox can still be seen if the letter A is turned upside-down: ∀. The second letter of the Phoenician alphabet is bet (which means "house" and looks a bit like a shelter) representing the sound /b/, and from āleph-bēth we have the word "alphabet" - another case where the beginning of a thing gives the name to the whole, which was in fact common practice in the ancient Near East.
The Glagolitic and early Cyrillic alphabets, although not consisting of ideograms, also have letters named acrophonically. The letters representing /a, b, v, g, d, e/ are named Az, Buki, Vedi, Glagol, Dobro, Est. Naming the letters in order, one recites a poem, a mnemonic which helps students and scholars learn the alphabet: Az' buki vedi, glagol' dobro est' means "I know letters, [the] word is good" in Old Church Slavonic.
In Irish and Ogham, letters were formerly named after trees, for example A was ailm (white fir), B was beith (birch) and C was coll (hazel). The rune alphabets used by the Germanic peoples were also named acrophonically; for example, the first three letters, which represented the sounds /f, u, þ/, were named fé, ur, þurs in Norse (wealth, slag/rain, giant) and feoh, ur, þorn in Old English (wealth, ox, thorn). Both sets of names probably stemmed from Proto-Germanic *fehu, *uruz, *thurisaz.
Modern radiotelephony and aviation uses spelling alphabets (the best-known of which is the NATO Phonetic Alphabet, which begins with Alpha, Bravo, Charlie, Delta...) in which the letters of the English alphabet are arbitrarily assigned words and names in an acrophonic manner to avoid misunderstanding.