Why do some people pronounce "singer" as "singGer"?

Solution 1:

The pronunciation of /ŋg/ where standard English uses just /ŋ/ is a common feature of many different varieties of English. Within the UK it is very common in areas such as Norfolk and Birmingham. It is also a feature of many varieties of USA English.

Learners of English quite often use an inserted /ɡ/ or /k/ after /ŋ/. The reason for this is that in many languages [ŋ] only appears as an allophone of /n/. This happens when the /n/ precedes a velar consonant, in other words /ɡ/ or /k/.