The world of politics is becoming increasingly-prevalent, and it is difficult not to have some knowledge about a topic that affects you as an individual. Hence, it is easy to for both the audience and the speaker to relate to. For the speaker, politics as an impromptu speech topic is good because the average speaker often is familiar with the counter-arguments used by his opposition.
Another topic easy to relate to is medicine. There are many issues and new advents in the field of medicine, which are diverse enough that an impromptu speaker can usually inform an audience in short time with little preparation. Topics might include drug research, water supply pollution or odd medical professions.
Like medicine, environmental topics are relevant to the average audience member. However, environmental issues are generally misunderstood. This makes the topic good for an impromptu speaker who has the opportunity to both inform and inspire action by audience members. Deforestation, overfishing and climate change are all provocative and interesting speech topics.
Anecdotes are usually the cornerstone of speeches on public safety. Often, an impromptu speaker can shed light on a topic that both informs listeners and connects with them, emotionally, by using practical stories. Good topics about public safety include high speed police pursuits, cycling safety, proper prescription drug use and gun safety.