Mayor Bloomberg is making the motions of acquiring another term. It breaks convention, because all the other state mayors only get two terms. His wish to abridge the New York constitution was a response to the entrenching financial crisis that's hitting America at the moment. Personally, I'm alright with it. It's not like he's declaring himself mayor again: he will be running for re-election, along with other candidates. He has experience, he done the city good during his terms, he knows his businesses, and because of the financial crisis, I'd think that he would be a best fit for a third term in office.
Term Limits of Government Positions
President of the U.S. > two 4 year terms
Vice President of the U.S. > limitless, theoretically
U.S. Senate > limitless 6 year terms
U.S. House of Representatives > limitless 2 year terms
Supreme Court Justice > limitless, until death
Governor of New York > two 3 year terms
Governor of California > two 4 year terms
Mayor of Los Angeles > two 4 year terms
Queens Borough President > limitless 4 year terms