This paper examines the ethical question, 'What is a good search engine?' Since search engines are gatekeepers of global online information, it is vital they do their job ethically well. While the Internet is now several decades old, the topic remains under-explored from interdisciplinary perspectives. This paper presents a novel role-based approach involving four ethical models of types of search engine behavior: Customer Servant, Librarian, Journalist, and Teacher. It explores these ethical models with reference to the research field of information retrieval, and by means of a case study involving the COVID-19 global pandemic. It also reflects on the four ethical models in terms of the history of search engine development, from earlier crude efforts in the 1990s, to the very recent prospect of Large Language Model-based conversational information seeking systems taking on the roles of established web search engines like Google. Finally, the paper outlines considerations that inform present and future regulation and accountability for search engines as they continue to evolve. The paper should interest information retrieval researchers and others interested in the ethics of search engines.