In most opinions Elvis hands down has sold the most records world wide. If you are looking at bands it is the Beattles. However, these estimations are based on the amount of albums which have gone gold and platinum. Single sales can not be accurately recorded. Also for a single album Thriller by Michael Jackson still tops everyone.
Michael Jackson's album, "Thriller" is the best selling album of all time. Its average number of speculated sales is over 110 million copies, and was released on November 30th, 1982.
It is currently Michael Jackson. If you are looking for someone alive, I think the beetles would qualify since there is still one member alive. Lady Gaga is slowly rising though, she may break the record.