Find Background Information
Part of developing your research question is finding relevant background information in your area of interest. This will help you:
 Learn basic information and vocabulary about a topic you might not know a lot about yet
 Determine the current status of research in your area of interest
 Decide if the topic you're thinking about is the right fit for you
See below for some ways to find relevant background information.
Encyclopedias, Handbooks, and Dictionaries

The Princeton Companion to Mathematics byISBN: 9780691118802Publication Date: 20080928Presents major ideas and branches of pure mathematics in a clear, accessible style. Defines and explains important mathematical concepts, methods, theorems, and open problems. Introduces the language of mathematics and the goals of mathematical research.

Encyclopedia of MathematicsOriginally published in 2002 by Kluwer Academic Encyclopaedia of Mathematics, published by Kluwer Academic Publishers in 2002 the Encyclopaedia of Mathematics is now open access. The European Mathematical Society, monitors and maintains editorial control over its content. Well referenced articles contain useful links to Math Reviews in MathSciNet.

MathWorldA free resource on math topics by Wolfram Research, makers of Mathematica. More akin to a math dictionary than an encyclopedia. References and direct links to Wolfram Alpha and animations.

For more, try this:
 Go to Tripod.
 Click the "Books and More" tab.
 Click the Advanced Search link.
 Enter math (or a word of your choice) in the top box.
 Enter encyclopedia or handbook or dictionary in the second box.
 Choose limits (such as location=Haverford or year of publication).
 See the example search below.
Blogs & News
Many excellent blogs exist and their value depends on what you seek.
Brie Feingold published an essay on the utility of blogs and cited outstanding examples for each purpose in MAA FOCUS. The article and the associated blogroll is an excellent place for finding just the blog you need.

Ars MathematicaMathematical concepts discussed with links to more technical parts in various encyclopedias.

MAA FOCUSMAA FOCUS is the newsmagazine of the MAA. It contains information about MAA activities, news about mathematics and the mathematical community, and lively articles about interesting new (or sometimes not so new) ideas in mathematics, mathematics education, and related areas.

Mathematical Communication BlogValuable resource for engaging students in writing and speaking about mathematics, whether for the purpose of learning mathematics or of learning to communicate as mathematicians. It originated from the M.I.T. Department of Mathematics.

Terry Tao's What's New BlogFields Medalist Terry Tao writes about open problems in Math, his own research and exposition on many interesting topics.
Also try browsing the current periodicals in the science library!