Good question!
Qualitative methods (QM henceforth) have become more widespread in the recent decades, according to a 2014's survey in the Journal of Economic Surveys. QM include, among others, in-depth interviews, focus groups, case studies, ethnographic studies, and mixed-methods (quanti+quali). They are still not that popular though, and have been very often looked down by the field. This is evident from the JEL coding, which does not include a specific section for QM, but does include one for quantitative methods.
In contrast to BB King comment, these methods have been used in very hard-core economic issues like Macro (e.g. Blinder et. al. 1998), Labour Economics (e.g. Cregan 2005), International Organisation (e.g. Autor, Levy and Murnane 2002), Development Economics (e.g. Valente 2011), etc (for more examples, see Table 1 in survey above). Here is an article from an MIT economist commenting on his experience with using qualitative methods in labour economics research (excuse the fallacy of authority).
If you want to explore more, there is a 2016's book dedicated entirely to the subject. Also, Chapter 7 of this handbook focuses on QM used in Heterodox Economics.
Other references in which QM are used:
