1970 = seventies
1980 = eighties
1990 = nineties
2000 = ??? gets confused
koolade
There was a lot of discussion on this subject way back in '99. Nobody ever came up with a good suggestion. We’re kinda stuck, I guess. Reminds me of the he/she thing. 
Peace,
mangeorge
Even the great Master Cecil couldn’t come up with a definative answer for this question http://www.straightdope.com/classics/a5_160.html
http://www.straightdope.com/classics/a5_161.html
both address this subject.
I didn’t check those links, but I’ve heard it referred to fairly often as “the oughts” (spelling?), since ought=zero. As in a 30.06 rifle is referred to as a thirty-ought-six. And how old people in movies referred to “ought six” or “ought seven” meaning 1906 or 1907. I’ve head newscaster frequently use “the oughts” to refer to the current decade.
You don’t think that sound’s a little silly?
Double Ohs?
I stand by my tennis inspiration and will insist on calling it ‘the loveties’. 
The noughties.
Or the naughties.
More tea, vicar? Oooh matron!
The time of No Joy.
I’ve been thinking that since 9/11. 
Umm . . . it’s quite obvious. “The Zeroes.”
Remember, you heard it hear first.
I must have been zeroed out. It’s called “surfing the Net too much:”
You heard it HERE first.
Since this questions has defied (at least as of yet) a definitive answer, I’ll shoot it over to IMHO. Maybe one of those guys can coin exactly the right one.
Dubya1
Dubya2
Dubya3
etc.
Yeah, that’ll work for now anyway…the “Dubyas”
ie: (future conversation) You remember, back in the Dubya’s…Let’s see, I think it was in Dubya3 that Iraq ceased to exist…hmmm
or was that DubyaDubya3 :smack:
The aughts.
Well, it’s obvious. No phrases are going to be coined here. No history made.
So please, Give It Up. We’re just not clever enough.
Besides, you don’t want to be the one to do what Cecil sat’s can’t be done.
The thousands
The Decade of Terror
But that’s a little depressing.
And a little ethnocentric… some of us have been dealing with terrorism for many, many decades.