Terrorism, the recession, and the rise of reality Tv are the ones that are unique or prominent to this decade I think.
Terrorism we have had for many decades before, and can expect for many decades to come. But nothing has come close in impact to the September 11th attacks. And hopefully nothing ever will.
Recessions again have happened many times. But they are pretty rare, and this one seems to be big.
Reality TV seems to be a distinctively 2000's phenomenon, although the seeds were planted much earlier. And it also seems to be in decline.
As for the ones I didn't pick:
War has happened a lot and will happen a lot. The past decade is not I think notable in that respect.
Global warming is an issue that I feel is longer than a single decade. There has been a lot of work on the science this past decade, but little political action, and little sign of major effects yet. The coming decade, or the one after, could well be the one where the effects become clearly seen, and/or major action to mitigate it takes place.
Political scandal doesn't bother me that much. To be honest what was pissing me off in the UK was not that the MPs were fiddling their expenses, but that the news media WOULDN'T TALK ABOUT ANYTHING ELSE. And I can't think of any other political scandals this past decade.
Environmental destruction (other than climate change) is again something I feel has not been a particular problem in the past decade compared to previous ones.
Diseases have been in the news a lot, but the only one that's actually a pandemic is the currently circulating H1N1 flu. It remains to be seen how severe it is.
Religious fundamentalism; again one I'm not sure is a specifically 2000s problem (though terrorism motivated by it was certainly a serious event).
The rise of the internet I attribute to the 1990s. Something that the 2000s has seen I think is the commercialisation of it, however. We entered the century with Geocities and Angelfire; we left it with Facebook and Blogger. I feel that is a change for the worse.
Other things that weren't on the list that I think we'll be remembered for. (These will be mainly science because that is my background)
Spirit and Opportunity, the Mars rovers. Possibly the most successful and inspiring space mission since Voyager, maybe even Apollo.
The USA electing the first black president in its history, of course.
The decade video gaming really hit the mainstream, thanks mainly to the Nintendo DS.
The Boxing Day earthquake and tsunami. 5 years ago to this day. As a natural disaster the death toll was terrible. As an earthquake it was extreme in scale, being the longest single rupture and the longest duration of faulting. It may have slipped out of the radar of the general public, but the geological community at least will talk about it for decades to come.
Hurricane Katrina, and the whole hurricane season of that year.
There are probably more that I have missed.
EDIT: @MrIndigo: 9-11 is certainly fairly well remembered in the UK, partly helped by TV
Besides, it's the sort of thing that will end up in every school history textbook in time. If the human race lasts long enough, in a few hundred years it will be another date for children to remember and repeat in the exams.
