In many countries an application for a PhD position includes a written research proposal, so my questions is what are some advises/strategies to come up with a good topic/idea for a PhD research proposal and how can one assess the quality/fruitfulness of an idea? As an undergraduate student one just doesn't have the experience to foresee which ideas might have promising research results and which probably won't have. (And I doubt that potential supervisors have the time to comment on every idea of every potential applicant in cases where it is possible to establish some kind of contact before the actual application.)
- Jot down your interests.
- Future goals (long term and short term). Doesn't have to be accurate but just to give you the "big picture".
- Speak with your PhD advisor (if you already have one).
- Align his/her interests with yours and see if you have common ground (you may need to lean towards his interests or find another advisor)
- Once you have a list of topics that you could explore, do a literature review and figure out for what topics you'd have a taste.
Each person has his own formula on what to choose as their PhD proposal. This was the way I went about it.
PhD (Mechanical Engineering Expected Fall 2012)
In your case, I would find scientific publications aimed at the student/general population in your field, and read the articles written for the public. Both Science and Nature will have numerous articles in each issue that can be read and understood by the general public. Some subfields have publications directed specifically at the student/enthusiast population (such as IEEE Spectrum for Engineering).
By reading through these publications, you will get a sense for what the current major research focus is in a wide variety of fields, and you'll get a feel for what's interesting to you.
Talk to professors in fields that interest you! You'd be surprised at how many professors (admittedly, not all of them) would be willing to spend 15 minutes talking to you about their research, and their field in general. I'm not going to say "showing initiative is key to making progress", because it's not, but it can help, and you'll learn a tremendous amount this way.
Find a subject that you really really are passionately interested in, and care about finding out more about it. This subject is going to become almost your entire life for a few years, and you will need huge dedication to it, in order to complete.
Talk, ideally over a coffee, but by phone or (worst-case) email if you can't meet in person, with people who recently completed their PhDs and are now actively researching in this field; discuss your ideas and recent developments in the field.
Find an area that your intended supervisor is up-to-date in.
If you do it right, your PhD will lead you to knowing more than anyone else in the world about this very very specific subject: so it will really help if you're going to be keen to pursue it as a career after completing your PhD, even after writing several papers and making plenty of conference presentations on it.
One aspect of a PhD is pursuing original research in your given field. I believe it is hard for an undergraduate to know what research has / hasn't been in covered in all of the topics they may be interested in.
Therefore, I would advise that you consider the topics you are interested in, and find out which Researchers / Professors are working in those fields, in the universities that you are considering. Then, you should ask them what they are working on at the moment, and what potential projects they would have in mind for a new PhD student joining them. This will give you a feel for the kind of research that you could be doing.
There are already very good answers above; I would only like to add that you should also take into account whether you can get a scholarship/funding for your research topic. Your personal interests may not necessarily align with those of your potential funders. Consider how much you would be willing to compromise your own interests to be able to receive a scholarship. Most people cannot support themselves financially through the course of a PhD programme, so this point is not to be underestimated.
If you apply for a government scholarship for example, they will likely want you to study a topic that is of high policy relevance to them and you need to think about whether you can offer that or modify your original ideas in such a way that they will meet the policy priorities of the government at the point of application. Governments tend to publish their strategic priorities in various documents online, so it will not be difficult to make the connections between your research and their needs.
University departments giving scholarships tend to be more flexible with regard to research topics as long as the quality and originality of the proposed research is high, but again, it would be best to get an opinion from a member of the department on the chances of your proposal attracting sufficient interest that it will get funding.
Without funding, it will be close to impossible to do a PhD.