Have there been 44 presidents in the US?

Yes. The 44th President of the United States is Barack Obama, 2009 - Present (2010).

No, including President Obama only 43 people have been U.S. President. The reason Barack Obama is called the 44th U.S. President is that they count Grover Cleveland twice (the 22nd and 24th President) because his two terms were non-consecutive.