My boss has started saying two zero one zero. I really do need to change jobs.
Why two-thousand-ten?+ Because it's the natural sounding follow-on to +two-thousand-eight, two-thousand-nine.
But 10 years or so down the road, after a decade of twenty-elevens, twenty-twelves, twenty-whatsits+, then +twenty-ten won't sound odd at all.

I'll be saying two thousand and ten just because I've got used to saying two thousand...?? in the last 9 years.
"How would you pronounce the year 1010?"
Double ten?
Seriously, to answer how I'd have pronounced 1010+ in 1009, I'd have to know how I'd been pronouncing 1009, 1008, etc., and I don't know (some of us aren't +that+ old). Perhaps it was simply +nought-nine, nought-eight, etc. Anyone know?
Take a look at this 2005 article in the Times of London. It's about "when will people stop saying "two thousand X" and start saying "twenty X"
Experts clash over millennium bugbear
Well into the 21st century it is still “two thousand and . . .” Will we ever be twentysomethings

889, I wasn't asking how some hypothetical you of 1009 would have pronounced 1010 -- it certainly wouldn't have involved noughts since it would have been written MX -- , I was asking how you today would pronounce it. So how would you pronounce 1010, say in the sentence "The Đại Việt era began in 1010 CE"?

From nutrax's link:
it seems that when naming years the world has become stubbornly determined to ignore a system that worked perfectly well for centuries
Has it really been centuries? Did people in 1789 say seventeen eighty nine or seventeen hundred and eighty-nine?
I've been looking at a number of contracts for 2013 and beyond, and almost everyone concerned is saying "two thousand and thirteen" etc almost all the time, although nobody looks askance at "twenty thirteen" which does pop up now and then.
However, it's easy to mis-hear, so people tend to stick to "two thousand and ..." when they especially want to be clear