I started following F1 only in this decade. Started as a neutral fan during 2001-2002 then turned into an 'anti' because of Ferrari/Schumi antics, then became a fan of Kimi from 2003 onwards.
For me things that stand out:
2002 Austrian GP: Staged finish where Rubens lets Schumi overtake him for the win. Most blatant display of team orders, where it wasn't necessary.
2003: Best season next only to 2007.
Kimi in his year old McLaren almost becoming the champion. Clearly he was the one to look forward in future.
2004 Belgian GP: Kimi won this, while rest of the season was dominated by Ferrari.
2005: Another year where Kimi almost became the champion.
The year was full of smoking McLaren engines every alternate weekends.
Kimi losing it in the last lap of European GP.
Suzuka, probably the race of the decade.
Alonso ending Ferrari dominance.
2006: Probably the most disappointing season for a Kimi/McLaren fan.
Ferrari engine blowing up in Suzuka which costs Schumacher a championship.
Schumi's last season (in this decade)
2007: Best (and worst) season of the decade. Best because of the way Ferrari and Mclaren traded wins and Kimi stealing WDC from McLaren boys.
Worst because of Spygate
Robert Kubica's crash in Canadian GP. I thought i had witnessed the worst. F1's high safety standards ensured that Kubica was racing again in 3 weeks time.
2008: Lewis almost losing WDC twice in a row. Emergence of Massa as a strong contender (Though he may not become a WDC ever)
Lewis-Kimi fight in the last 3 laps of Belgian GP, only true racers can produce something like that!
2009: Brawn pulling off a miracle.
The year that saw usual winners struggling to even score points in most races
Belgian GP: Kimi's last win (unless he makes a comeback and wins again)
Force India taking a podium in Spa, and promising good results in future.
To watch out in the new decade:
Will Schumi add more to his already huge tally of wins and WDCs?
Will Kimi make a comeback?
Lewis/Alonso renewing their battle in two of the most popular teams in F1
Will Vettel/Rosberg/Kubica challenge the top guys?