Most letters were once pictures that were stylized and ended up being shorthand for what they depicted. In fact, it's very hard to find any letters that aren't originally pictures. Norse runes qualify, as do the Phoenician-based alphabets (which are almost all of them). Even in Cyrillic, many of the extra letters were actually stolen from Coptic, such as the щ, from the Coptic cаще, "field". It depicts rushes growing and is a stylized form of the Egyptian hieroglyph. The same goes for ч, though in that case the phonetic value radically changed (from /f/ to /ch/). And, of course, the rest came from Greek.

In the case of "ng", although it appears to just be a variant of an existing letter, it was totally unnecessary and made up out of whole cloth. The combination of n+g had already been used for centuries and there is no word pair in which the sense changes if the n+g is nasalized or if the g is actually pronounced. Hence, it's a made-up letter.

Finally, other letters that have been created as variants of existing letters are created to symbolize a sound that doesn't exist in the language the alphabet is derived from. In the case of "ng", that's also not true.