[edit: As i understand it, the only real "need" for flash (as a browser player plugin) is that associated with DRM-regulated video. Everything else it does (which one might deem as being vital) can easily be replaced. And again, everyone who likes to whine about google and facebook tracking their movements should keep in mind that flash does that stuff too.]
It's also needed for certain types of interactivity. Complex games with scripted actions, for instance, can't (yet) be done in pure HTML.
However, as time goes on, I think that will be less and less the case.
