Here are some online resources I frequently use during research:
The invaluable Useful inequalities cheat sheet This page has been crucial for at least one of my papers (so far).
Detexify For when I cannot remember that obscure LaTeX command.
TeX Stack Exchange For my infinite Tikz questions.
Some textbooks which I enjoy or use frequently.
Analysis of Boolean Functions by Ryan O'Donnell.
Algebraic Graph Theory by Chris Godsil and Gordon Royle.
The Probabilistic Method by Noga Alon and Joel Spencer.
Generatingfunctionology by Herb Wilf. A classic.
Finite Model Theory by Leonid Libkin. A great reference for all things finite model theory, and quite readable also.
Boxes and Diamonds by the Open Logic Project. A fun little book introducing modal logic in a down-to-earth fashion.
Early in my undergraduate studies, I became interested in category theory, and have slowly been self-teaching the subject ever since. Here are the resources that have been quite useful:
Haskell. In my first semester of undergrad, I fell in love with both proof-based mathematics and computer programming. I also experienced the deep and abiding frustration of debugging my own code. Lo and behold, I was delighted to learn of Haskell, a programming language built by mathematicians. So began four or so years of attempting to decipher the peculiarly terse syntax (the wiki has some excellent examples) and awe-inspiring type system. Eventually, these little side programming projects led me to full-blown category theory.
Entropy and Diversity by Tom Leinster. From Leinster's book came my interest in Magnitude Homology.
Sheaf Theory through Examples by Daniel Rosiak. This book convinced me that a mere mortal such as myself can actually understand sheaves.