Do you remember the other Year 2000 problem, regarding the nicknames of the years? If 1999 was "ninety-nine," then what would we call 2001? At the time, answers such as "one", "oh-one", "two-oh-one" and even "naught-one" were suggested. Now, with well over a decade of experience, what conclusion have we come to, if any?
I think 2001 will remain two-thousand-and-one and from 2010+ it will be twenty-ten, etc. The 20th century has it's special short-hand versions, but I think in the future it will be the twenty-eighties not the eighties.
We use the term "thousand" (mostly without the "and" for the sake of brevity) when citing the full year:
And we use "oh" before the single digit for the short form:
2011 provides a unique challenge. I hear it split fairly evenly between "two thousand eleven" and "twenty eleven" whereas 2012 most always falls out as "twenty twelve"; I attribute this to the odd middle-accented "eleven" more than anything. It's an awkward word in combination, which is why it often is used for humorous effect ("eleventy-twelve" and the hobbit meal known as "elevensies").
Now that we're in the tweens, the twenties rule: twenty thirteen, twenty fifteen, etc. It's just shorter and easier to say.