SIMBAD - find data and publications associated with almost any celestial object.
VIZIER - find catalogued data in a huge online library.
The Smithsonian/NASA Astrophysics Data System - search for astronomy abstracts, with most full papers being online.
SkyView virtual observatory - download images of any patch of the sky - in a multitude of wavelengths, and with catalogue overlays.
StarAlt - determine the visibility of targets from anywhere on Earth.
Minor Planet Center - keeps track on all those asteroids, and more.
NIST atomic line list - high-quality atomic data.
StatPages.net - a large selection of java based statistical tools. In particular, I've found the binomial confidence interval estimator very useful.
arxiv.org/astro-ph - online e-preprint service. Keep up-to-date with the astronomical literature by visiting this link every day!
The Star Formation Newsletter - collects the most relevant abstracts in the form of a monthly newsletter.
European Southern Observatory - homepage of the most influential observatory.
Las Campanas Observatory - home of the Magellans.
Gemini Observatory - with telescopes in both hemispheres.
Stockholm Observatory - where I got my Ph.D. in Sweden.
University of Toronto - a previous home in Canada.
Sky Tonight - astronomical newswire.
Astronomy picture of the day - every day, a new amazing picture of the universe we live in.
StarStrider - a 3D planetarium software I wrote together with my friend Markus Dimdal.
eightplanets.org - loads of information of the eight planets in our solar system, and more.