If you want basic diagrams, and not so-basic ones, consider LibreOffice or OpenOffice. Their dwawing and slideshow apps have simple but nice diagraming features, many styles of conectors, you can move shapes around and they stay connected. Also can import shapes designed to Visio, and although they come with a very small set of default shapes there's dozens more available for free download by the community.
Other features are high-quality (for printing), web optimzed, protected and encrypted PDF export, besides export to Flash, SVG, EMF and other vector and bitmap formats.
I use them for many kinds of flowcharts and network diagrams, never felt the need for a "better" tool, but I found other tools cited in the article to be counter-intuitive or to produce very ugly diagrams.
Other option worth evaluating is the Kivio tool from KOffice. I guess the suite and the diagraming tool changed their names recently and they also got a decent Windows port. I liked it when I tried a few years ago, but LibreOffice was enough for my needs and has already supported both Windows and Linux for many years.
Keep Up with TechRepublic