(DYADS, TRIADS, & QUADS, oh my!)
Sometimes the anonymity of the typical eight-respondent focus group gets subjects to open up in ways they never could otherwise. But with some projects, either because of the sensitivity of the topic or the age of the respondents, more intimate groups are more insightful. These smaller groups allow each respondent to express him- or herself more fully and completely, and allow us to probe more deeply.
These are also known as "buddy groups": talking with people who already know each other pre-research. They're recommended whenever you need to understand the actual dynamic of the cohort itself (e.g., how Millennials interact with each other). They are also especially valuable when researching younger kids (<7), who are much more confident and expressive when surrounded by friends.
One-on-one interviews can be appropriate for very sensitive or personal topics, when you need to understand how consumers might use something in an observable setting, or when your target is highly professional (i.e., Dr., CEO, etc.). While effective, they are not as efficient as other qualitative techniques, so they should be used sparingly.