According to Wikipedia, Princess Diana's funeral attracted the largest ever global television audience for any non–sporting event.
Top of Wikipedia's list, with a worldwide audience of 3.6 billion, are the 2012 and 2016 Olympics. They are followed by other Olympiads, other sporting events such as FIFA and Cricket World Cups, and two Muhammad Ali fights (v. Leon Spinks in 1978 and Larry Holmes in 1980). Princess Diana's funeral comes in at No. 28 with a global audience of 2 billion. (On the page for the funeral itself, Wikipedia gives an estimated global television audience of 2.5 billion, which would put it at No. 16.)
In the UK, Princess Diana's funeral is second only to the 1966 FIFA World Cup Final (32.1 million as compared with 32.3 million).
Wikipedia begins its History section by stating that the Apollo 11 moon landing (on 20 July 1969) was viewed by an estimated 3 billion people – which, it points out, was 45% of the world population at the time; it was the middle of the night in Europe, and it wasn't even shown in the Soviet bloc. It cites two sources for this statement, but I can't find such a figure on either. In fact one of them mentions a figure of 600 million, and the other (NASA's own website) gives 650 million. Wikipedia concurs with the former figure (600 million) in its Records section, citing yet another source (a printed book).
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