The Linneaen system is actually outdated at the moment, but I think that you can say with pretty high confidence that there are 3 "kingdoms": Archaea, Bacteria, and Eukaryota. And then there are the viruses, but nobody's really sure just what the hell they are or where they came from, because they evolve so quickly.
The most up-to-date website, although it claims not to be comprehensive in any regard, is the NCBI Taxonomy site: http://www.ncbi.nlm.nih.gov/Taxonomy/Browser/wwwtax.cgi?mode=Root. But if you're a complete beginner, then the best place to go exploring is the Tree of Life: http://tolweb.org
Oh, thanks for those! The TolWeb site looks just right for me at the moment (although I think I'll eventually spend lots of time at both): Lots of footnotes and links to other sites, which I always appreciate. This stuff has always been confusing to me. Thanks again. Cheers!