In many cases, instructors at schools or colleges will provide some specific guidance into research essay topics. If not, the best topics depends on the type of course you are in, what you are studying, and what you hope to learn from conducting the research. Though most research essays are related to academic work, some people choose to write and publish research essays on their own volition, based on whatever field they choose to work in. In general, the best research essay topics ask a question where both sides have valid arguments; this makes the essay more interesting, and also forces you to fully explore both sides of the issue.
Usually, research essay topics do not spring forth from nothing. They will come from the type of work you are doing, such as a text you're reading or some other area of interest. In schools, teachers will often allow students a fairly large range of topics so the students choose something based on their existing interests, which will ideally make them more enthusiastic about the project and motivated to complete it. If this is the case, think of the things you do in your spare time; for instance, do you enjoy playing sports, or learning a musical instrument? Chances are you can find a research essay topic in there somewhere.
The purpose of writing this way is usually to explore a question deeply, and then use the paper as a platform to make a strongly supported argument. This means that it is necessary to think critically about the text or issue you are considering researching, and identify an area in which people might have differing opinions, or in which additional information could prove or disprove a point. Take care to narrow your topic down to something that can be explored detail within the alloted length; research essay topics that are too broad tend to result in shallow papers that are unlikely to be well received.
In general, it is a good idea for anyone who knows that he or she will need to come up with research essay topics to start thinking about this as soon as possible. For instance, if you start a class and know there is a research paper due at the end of the semester, keep it in the back of your mind through the class. If a particular lesson or text fascinates you, or you have specific questions, make note of these throughout the class and you might just find a research essay topic. Once you have an idea, do some checking around to see if there is enough research available on your topic, or if you need to keep looking.