Generally Useful
London Mathemtical Society Funding for PhDs occasionally advertised here, as well as seminars and maths-themed events.
Institute of Mathematics and its Applications Useful maths-related resources for any stage of your studies.
The Clay Mathematics Institute If you don't know about the Clay Institute and what they do... go and and out now!
UCL Maths The main UCL Mathematics Website; you should be familiar with it. Look here for module choices.
UCL Maths Colloquium Weekly talks from UCL Maths students for UCL Maths students.
Maths Reference Useful Maths search engine. You will know what I mean if you have even search for a "Ring" or "Field" in google.
The American Mathematical Society If you are genuinely interested in a Maths career/further studies then this website is very useful. It's American but there is a lot of general information as well.
Work in Academia
Maths Jobs Wiki Currently advertised jobs in academia (Maths) all around the world.
Jobs dot ac dot uk General website for jobs in academia, research and science.
Undergraduate research internships
EPSRC Vacation Bursaries Funding for Undergraduate Summer Research Projects.
LMS/Nuffield Foundation Bursaries More potential funding.
CoMPLEX at UCL Interdisciplinary research opportunity at UCL. Maths into the Biosciences.
Summer Research at the University of Kent Open to all Maths students in their penultimate year.
Summer Research at Oxford Last year's page. Similar to above.
UROP at Imperial Imperial allow outside students to do paid summer research there if they can find a supervisor.
Maths Resources
Interesting Maths Blogs
Stack-exchange list of Blogs A good place to start if you are interested in finding good maths blogs.
Terrence Tao's Blog Even if don't understand anything, it's useful for finding out about the real maths word, as well as finding many other blogs.
Computational Help
Wolfram Alpha Extremely powerful computation engine. See also Mathematica available free to UCL students.
PARI/GP Computations in number theory and others.
Mathematics Forums
Math Stack Exchange Lots of threads about all kinds of maths question. Do not abuse it for homework purposes. Lots of lecturers actually also follow it.
MathOverflow Similar to the above.
Online Lectures and Courses
Coursera Online courses in maths and other subjects; many of them give certificates for accomplishment.
Edx Similar to the above
MIT OpenCourseWare MIT put most of their courses online. Many of them have video lectures. For example, you can find Algebra and Calculus lectures.
Other Online Courses Comprehensive list of MOOCs (Massive open online course) if case you ever need more.
LaTeX Resources
TeXmaker Probably the best TeX editor you can find.
Write LaTeX Online Real Time TeX Editor.
CTAN Packages and all sorts of useful thing.
Texample Examples of things created in TeX and free source code to use.
TeX Stack Exchange Question/Answer help forum for TeX.
LaTeX Wiki One of the best references online.
Resume Templates Good for CVs; you can just take a template for free and edit it to get a nice-looking CV.
LaTeX Templates Some more nice templates, including for CVs.
GmailTeX Plug-in for using TeX with gmail
Random Things
PhD Comics Silly Comic.
xkcd Slightly Silly Comic.
SMBC Very Silly Comic.