Mathematics
 Math StackExchange, a Q&A forum for math of any level (homework problems welcome, if you explain what you've tried so far)
 Tricki, a wikistyle collection of mathematicians' favorite problemsolving tricks and techniques
 How to Solve It, by George Pólya
 10 Ways To Think Like A Mathematician, by Kevin Houston
 Math Reference Project, maintained by Karl Dahlke
 A Mathematician's Lament, by Paul Lockhart
TeX / LaTeX
The document preparation system LaTeX is almost universally used to create mathematical and scientific works. Here is an explanation of what TeX and LaTeX are, their history, and the benefits of using them.
 TeX StackExchange, a Q&A forum for all things TeX and LaTeXrelated
 TeX Resources on the Web, organized by the TeX Users Group
 LaTeXiT, a LaTeX equation editor
 Detexify, a website to help you find the LaTeX symbol you're looking for
 TeXnicCenter, a Windows LaTeX editor
 Kile, a LaTeX editor for KDE

GmailTeX, a plugin for Gmail that compiles TeX / LaTeX code in your emails
Computation
 List of software that is available using a license from Brown (includes Mathematica, Maple, and Matlab)
 Mathematica StackExchange, a Q&A forum for Mathematica
Programs for Undergraduates
Brown offers Undergraduate Teaching and Research Awards (UTRAs). Applications for summer UTRAs are typically due in early February, so you should definitely talk with the professor you'd like to work with before winter break.
Outside of Brown, many summer math programs are what are known as "Research Experiences for Undergraduates" (REUs). These are designed to give you a sense of what real mathematics research is like (though the specific format can vary greatly). Many programs will require one or more recommendation letters, and it is good to give professors some time to write these.
 Some advice from the MAA: Is An REU For You?
The following summer programs give you an opportunity to encourage younger students to pursue their interest in math.
 PROMYS, an excellent program for high schoolers at Boston University, focusing on number theory
 The Ross Mathematics Program, held at Ohio State University (PROMYS is a descendent of the Ross Program)
 HCSSiM, a program for high schoolers held at Hampshire College
 Center for Talented Youth, a network of summer programs run by Johns Hopkins University
There are also semester and yearlong math programs for undergraduates. Here are some of the betterknown ones:
 Mathematics Advanced Study Semester (MASS) at Penn State
 Math in Moscow (see this scholarship offered by the AMS)
 Junior Program at Smith College's Center for Women in Mathematics
Applying to Graduate School
 Career advice, by Terence Tao
 Some good fellowships to apply for:

Some advice on how to apply for those fellowships:
 Applying for Graduate Research Fellowships, by Seth Sullivant
 Advice for applying for graduate science fellowships: NSF, NDSEG, Hertz, by Philip Guo
 Fellowships and Funding advice from Cornell Astronomy (most of it is relevant to all subjects)
 Advice on applying for the NSF fellowship, by Kevin Sanft
 Some graduate school links on the AMS's website.
 Assistantships and Graduate Fellowships in the Mathematical Sciences, a document compiled by the AMS each year
 Preparing For Grad School, advice from MIT
 How to get a great letter of recommendation, by Matthew Might
 Recommendations, by Ravi Vakil
 Get into grad school for science, engineering, math and computer science, by Matthew Might
 Thoughts on graduate school, by Noah Snyder (an addendum by Ben Webster)
 More advice for prospective graduate students, by Noah Snyder
 A Graduate School Primer (MAA), by Doug Faires
 Choosing a graduate school, by Diana Davis
 Tips for Visiting Grad Schools, by Kimball Martin
Organizations
 Young Mathematicians' Network (their site is currently under construction)
Miscellaneous
 Obvious But Underappreciated Truths, by Alan Stein
 The History of Mathematical Symbols, by Douglas Weaver
 Science Lives Project, a series of interviews with famous mathematicians and scientists