I agree with Larisa that interviewing until saturation is achieved is the most common standard for determining the sample size in qualitative research. If you are using focus groups, this would mean conducting groups until they become repetitive, such that you are not hearing anything new (i.e., not getting any further data).
As mentioned in the answers above, sample size depends on reaching theoretical saturation. However, it is not practically possible to have big sample size comparable to quantitative research. Qualitative research will provide with rich data even with small sample. Rigorous and careful simultaneous analysis and constant comparison will help you to reach the goal and control.
What sample size is sufficient in a qualitative research?
There is no fixed rule of thumb but depending on your research requirement. E.g. some research only need 1 sample / interviewee so that the researcher can interview him / her until data collection saturation (meaning interview will stop when no new information or repeated information is received). Some research need multiple sample / interviewees / cases e.g. in focus group & case study until data collection saturation.
Even if the concept of saturation is ideal one needs to have a tentative sample size to start with as the initial. this initial sample size is based on the type of qualitative study chose. for example if one is doing a phenomenological study the guiding sample size to explain the experiences has been established to range from 8 to 15 participants and in theory this has been established to provide insights of experiences, but saturation may be reached way before the initial number or it maybe reached after the established sample size. In simpler terms, always start with a tentative sample size as guided in literature and use this sample size for you to reach a theory in your study ( Theoretical Saturation).