This is a very broad question, but I can answer it from my own background.  I have worked as a scientist in a research institute (at NASA) and have a PhD and both of these required that I deal with this question in a very big way.  I'll try to keep this brief :).

In its purest form, research should address unanswered questions and unsolved problems.  The research then is to find answers and solutions.  If you know the answer to every question, then you're stuck.  But no one does.  One good source of topics is the "Areas of Future Research" that usually occur at the end of most research papers.

Another source is your academic advisor or teachers.  They should be senior enough to know what are the open (and interesting) questions in your field.

THis does not apply to most people, but another good source of research topics are funding agencies.  Government and non-government organizations frequently send out announcements of funding for research topics.  The National Science Foundation (NSF), the Defense Advanced Research Projects Agency (DARPA), NASA, NIH and NIMH are ones I have worked with in the past.

For someone trying to devise, say, a science fair project, it is harder because almost everything has been answered.  Pick a topic that is of interest to you, because doing a project is a lot of work and if the topic is not interesting, keeping your motivation up willbecome taxing.