Soccernet has a great little list up of The Greatest Goals of the Decade. Only problem is, they don't have videos. But I (whose attitude to copyright is dubious at best) do.
So here they are.
Paolo Di Canio
West Ham v Wimbledon, 2000
I once got Youri Djorkaeff to do this in FIFA99 on my computer. I didn't think it was possible in real life.
Rivaldo
Barcelona v Valencia, 2001
Gianfranco Zola
Chelsea v Norwich, 2002
Dennis Bergkamp
Arsenal v Newcastle, 2002
And before you ask, his goal against Argentina happened in the 1990s.
Zinedine Zidane
Real Madrid v Bayer Leverkusen, 2002
Read the Soccernet write-up about this for a full appreciation.
Jared Borgetti
Mexico v Italy, 2002
I remember watching this and thinking, "So what?". Then I saw the replay.
Zlatan Ibrahimovic
Ajax v NAC Breda, 2004
Estebian Cambiasso
Argentina v Serbia, 2006
Lionel Messi
Barcelona v Getafe, 2007
The Soccernet piece talks about the similarities with Maradona's goal in 1986. This video clip explores that further. Scary.
Grafite
Wolfsburg v Bayern Munich, 2009
It's not as great as Sebastian Langkamp's classic, but it's pretty darn impressive nonetheless.