Eng seems to be a very popular letter. So far I have been able to identify 101 languages which have (or had reasonably recently) eng as a member of their alphabet. Eng languages make up very nearly 17% of the nearly 600 languages in the Cedilla database at the moment.
Wikipedia tells us that the letter was designed by Alexander Gill the elder in 1619 as part of his attempt to revise English spelling. He also proposed reviving the use of Old English <þ> and <ð> to represent the voiceless and voiced versions of <th>. Gill’s proposals met with no success, although his new letter was adopted by Benjamin Franklin in his Phonetic Alphabet.
PNG=Papua New Guinea
The chart above gives a rough idea of the geographical distribution of <ŋ>. The “other” category includes languages scattered around the globe, in Europe (the different varieties of Sami), Australia (Yolŋu), the Caucasus (Chechen), China (Zhuang) and Central Asia (Tatar) and South America (Purhepecha). You can see the complete list by navigating to Cedilla (link in sidebar) and clicking the relevant button.
In the vast majority of languages which use it <ŋ> represents a voiced velar nasal, which is what Gill intended and what Franklin used it for. There is at least one puzzle, however. The short-lived Chechen New Latin alphabet, introduced in 1992, but banned after the defeat of the secessionist government, contained <ŋ>, but Chechen seems not to have an /ŋ/ phoneme, so I am not sure what it was used for. Some Cyrillic alphabets (not included yet in Cedilla) I have come across use <ŋ> to represent /ə/.