Various portions of HTML5 are supported by the different browsers, for various definitions of 'supported'.
Several parts work right now, reliably. The data-* attributes you ask about in your question work just fine in every browser, even IE6; however, nobody yet supports the fun "dataset" method to access them. As long as you're fine with just grabbing them by the full attr name, you're golden. I use them to store state all the time in my webapps, as they're the officially blessed method for doing so.
Wikipedia has a good summary of the various support levels across browsers: http://en.wikipedia.org/wiki/Comparison_of_layout_engines_(HTML_5)
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