Here are some of my favourite links:

• www.mathpages.com, can keep you absorbed for hours.
• Preprint server, a very very useful site. If you are a mathematician and do not submit your papers here, please consider doing so in future -- your papers will be read by more people, and more importantly, by those who can not afford to buy expensive journals.
• John Baez's home page. I would specially recommend "this week's finds in mathematical physics".
• Sci.math.research
  
• Official string theory web site.
• This page will give you some idea as to what a good thesis problem should be like.
• cut-the-knot.
• Biographies of mathematicians, past and present.
• History of mathematics.
  

Homepages of some mathematicians:

• Terence Tao
• Timothy Gowers
• James S. Milne, try his "tips for authors"!
• Paul Baum
• Nigel Higson
• Allen Knutson