At my college, in the American Studies dept, there are classes on each decade of the 20th c. 100 years from now, what events will be taught about the aughts?
How file sharing (specifically Napster) and to a greater or lesser extent (I’m not sure) the invention of MP3 Players changed the music industry.
I know both showed up at the very tail end end on the 1990’s but they really took off in the 00’s and the music industry certainly didn’t react until the 2000’s. The only reason you might not be able to discuss it as a 00 topic is because I don’t think they’re quite done reacting.
Same Sex Marriage becoming legal (not everywhere of course, but in the 2000’s is when it started)
Obama taking office as the first black president.
9/11
I’d add Katrina, the 2000 election, and the financial meltdown.
The 2009 stock market crash was the next thing I was going to add on, I was just about to go and look to see how ‘crashy’ it was in the grand scheme of things.
9/11
The election of the first black President
The war in Iraq
The first time the notion of anthropogenic climate-change really became a topic of public interest.
The rise of radical fundamentalist Islam (including, but not limited to Sept 11th 2001).
I was going to mention that, and had a few others typed in a post. But then I remembered the OP said:
(bolding mine)
Because the tsunami made news here, along with Fukushimi, they’ll be mentioned.
9/11 will be the first thing. Obama the second. Katrina, Iraq, even Afghanistan, gay marriage will be footnotes. A Supreme Court that has will do everything possible to keep the court in the hands of the conservatives will join with the court of the 30s as the most hidebound. The current “recession” seems to me to be getting to be as long and intransigent as the great depression. I will not consider it over till the unemployment rate drops below 5% and this will very hard because the more it drops the more people who have given up even looking will start to again.
I suspect that over the next few decades that rehabilitation will become more of a working science and will expand into mental healthcare and self improvement in general. Breakthroughs will be made on the rewiring or our brain circuitry and the world will become a different place because of it. Instead of being the iron age or the computer age it will be discussed as the blankety blank mind rehabilitation age.
In my experience, college-level history classes focus more on trends than on actual events.So: social media, smartphones, Google, the NSA … all that pre-Singularity stuff. Everything else will be just background noise. The Iraq War will be remembered about as much as the Philippine–American War is remembered now.
A key sub-specialty of 2000’s historians will be Kardashianology.
I’m kidding (of course) but I could see the word “kardashian” being used in the future as a noun meaning: “something with no value or importance that is nevertheless incorrectly perceived by many people as being noteworthy, meaningful, or useful.”
Example: “The inventor’s purported perpetual-motion device was purchased by millions of consumers but, unsurprisingly, turned out to be a total kardashian.”
The terrorist attacks of September 11, 2001 will be familiar to a fair number of academic historians and to a few trivia buffs, but it’ll be unknown by your average schmoe after being eclipsed by some event an order of magnitude more devastating. Probably the detonation of a nuclear device by terrorists or a rogue state.
If my experience with general history classes is anything (ie petering out shortly after WWII), by 2100, they’ll finally be covering the 1950s. 
Do these terrorists have access to a time machine? The OP is asking about a hypothetical class focused on the years 2000-2009.
History is about what’s important to the people writing it, not the people living it.
The 2000’s will be taught as the beginning of the Second Gilded Age where the rich got fabulously richer and the economy stagnated for everyone else. This will be important so students understand the context of the populist revolts of the 2020’s.
9/11 and the invasion of Iraq will be taught as skirmishes in the Oil Wars. The extent to which international politics revolved around controlling access to petroleum will be hard for students in the post-oil era to grasp.
Paris Hilton can’t even get this term named after here. Talk about a total kardashian.