Basic Astronomical Data:
http://simbad.cfa.harvard.edu/simbad/ - One of two equivalent sites hosting the SIMBAD database, which contains key information on a vast number of stars and some other astronomical objects
http://simbad.u-strasbg.fr/simbad/ - This is the primary host for SIMBAD, but the two sites are equivalent (unless a server is down at one of the sites).
asa.usno.navy.mil - The online version of the Astronomical Almanac, co-published by the U.S. Naval Observatory and a comparable institution in the United Kingdom.
http://www.astro.umd.edu/~ssm/ASTR620/mags.html - A compilation of information about photometric bands and conversions among them. Scroll to the bottom of the page for a humorous touch.
Current Sky Phenomena:
www.astronomy.com - The website of one of the two main popular astronomy magazines. If you don't see “Sky This Week” on the cycling display, click on the link by that title on the Observing menu, under either Recent Headlines or Topics.
www.skyandtelescope.com/ - The website of the other major popular astronomy magazine. Look for “This Week’s Sky at a Glance."
http://stardate.org/nightsky - StarDate magazine, website, and radio spot are produced by McDonald Observatory's Public Information Office.
http://outreach.as.utexas.edu/public/skywatch.html - From UT Astronomy; gives current star party information as well.
Sky simulator software:
www.stellarium.org/ - popular and free
www.sky safariastronomy.com/ - Available as apps for your smartphones or laptops
www.worldwidetelescope.org/ - provides multi-wavelength images obtained with a range of instruments including space-based telescopes
http://star-www.st-and.ac.uk/~fv/webnotes/index.html - This site, created by Fiona Vincent of the University of St. Andrews in Scotland, U.K., provides a very nice and diagram-rich tutorial on spherical geometry and astronomical coordinate systems.
http://www.cv.nrao.edu/~rfisher/Ephemerides/earth_rot.html - A detailed but concise description of factors contributing to the slow changes in the equatorial coordinates of objects in the sky due to drift in direction of the Earth's rotational axis.