What role does ethics play in social science research? What are some examples of research that presented ethical dilemmas for the researcher?

In considering this question, it is important to first consider the types of research commonly used in social science research: qualitative and quantitative research.
Qualitative research is exploratory. It investigates the reasons that things happen, the interactions between forces, the motivations between actors, and similar phenomena in order to develop hypotheses regarding the problems in society and possible solutions. Quantitative, on the other hand, relies on statistics and data to make determinations about these issues.
As these research methods require different research processes, they evoke unique ethical issues: qualitative research deals with the ethical treatment of subjects while quantitative research raises issues of the ethical treatment of data. I have briefly outlined the issues and provided sources for further information below:
In qualitative research, researchers have direct contact with human subjects and their stories. This raises issues of confidentiality as well as the manner in which the researcher interacts with the subjects. For more information, please refer to Qualitative Research & Evaluation Methods by Michael Patton. For a more in depth analysis of the ethics of qualitative research, particularly the lines to draw in immersing oneself in their research and related issues, please refer to Every Twelve Seconds by Timothy Pachairat.
In quantitative research, researchers handle raw data in order to make determinations about the subject. In doing so, they frequently have the opportunity to mislead using seemingly concrete data. The researcher has a responsibility to only use data to illustrate the truth. For more information, refer to The Handbook of Social Research Ethics by Donna Mertens and Pauline Ginsberg.
For more information about ethics impacting both qualitative and quantitative research ethics including the ethical design of studies, please refer to Research Design by John Creswell.