Dream no longer, because the first step toward realizing a Flash-free internet is here. YouTube has introduced an HTML5 beta. The formerly Flash-laden site, whose popularity most likely led to the profusion of Flash on the internet within the past few years, can now be viewed without using Flash at all if you opt into the beta.
The HTML5 option is only available for browsers that support HTML5 (obviously) and h.264. Safari (version 4 and above), Google Chrome, and Internet Explorer with Chrome Frame are a few of the qualified browsers.
There are a few caveats to the HTML5 beta. Videos with ads aren't supported (awww...) – they'll play in the standard Flash player instead. There's also no support for full screen; clicking the little expander button on the lower right corner of the video will instead expand the video within the window to about double the normal size. Honestly, YouTube's full screen video has never impressed me much anyway, so this isn't a huge loss. Macworld notes that you also lose support for annotations and closed captioning, though, which might be a deal breaker for some.