SHORT ANSWER
Has any music act ever topped the Beatles in sales?
There is probably only one likely contender - Elvis Presley - but it is highly unlikely that we'll ever know for sure.
One problem is how to calculate sales (i.e. singles vs. EPs vs. albums vs. double albums vs. music videos vs. streaming). Another problem is the reliability and completeness of data from record labels. As Spencer has pointed out in a comment below, citing sales value would seem to be the logical way to get around the first problem, but such data does not appear to be available. The music industry has traditionally cited sales in units and recording companies are cagey about value (and have also been known to inflate figures for units sold).
COUNTING PROBLEMS
There are numerous problems in arriving at a total, not least of which is how sales of albums and singles are counted. Should one album sale be equivalent to one single sale, or to the six, eight, ten or even twelve singles that can fit on one album?
Also, how does one count the numerous multi-artist compilation albums that include one (or maybe several) songs from the Beatles or Elvis Presley (or whoever else one is trying to tally the sales of)?
And how can one be sure of numbers when some record companies refuse to release sales figures, while others may well be inflating numbers for publicity reasons?
These are just a few of the problems...
THE NUMBERS
Of the more than 30 sites I've looked at which give estimates, very few cite any sources or explain how the numbers they quote were arrived at. For what they are worth, here are some examples (roughly from highest estimates to lowest).
For those who want the most realistic data, go to headings 3 & 4 below.
1. 'Hard to believe'
The Beatles: 1.6 billion singles sold in the US + 600 million albums worldwide. Source: Beatles by the Numbers. These numbers are also given by cbsnews.com (2014). Of all the numbers cited, this 1.6 billion US singles is the most suspect. Even 1.6 billion units worldwide would be hard to believe so this estimate seems to be fanciful at best.
Elvis Presley: 1.5 billion, according to Sony BMG (circa 2016). Source: For The Billionth And The Last Time : Lifting the Lid on the King's record sales. The author of this article disputes this figure and, as with the Beatles 1.6 billion, seems unrealistic.
2. 'Just a convenient round number?'
Elvis Presley: "sales of Presley records have passed that coveted one billion milestone" (2016). Source: For The Billionth And The Last Time : Lifting the Lid on the King's record sales
The Beatles: Over one billion discs and tapes (EMI estimate, March 2001). Elvis Presley: 1 billion sales worldwide. Sources: Best-selling group and Best-selling solo artist
Elvis Presley: 1.1 billion, Bing Crosby: 900 million. Source: The Elvis presley - Bing Crosby Comparison Page
Michael Jackson: 1 billion (Dec 2015). Source: Michael Jackson's 'Thriller' First Ever 30X Multi-Platinum RIAA Certification
Bing Crosby: "close to one billion records, tapes, compact discs and digital downloads around the world." Source: Bing by the Numbers. His Amazing Music Records
3. Probably more realistic (but method of calculation not explained)
The Beatles: 545 million units worldwide (October 1972). Source: Beatles Record Sales Around The World, citing Billboard 84, October 21
The Beatles: 257.7 million, Elvis Presley: 206.8 million. Source: Top-selling artists worldwide from 1954 to 2016, based on certified sales (in millions). Note: this site does give a source but it is hidden behind a paywall.
4. Probably more realistic (with method of calculation explained)
The Beatles: 419,531,000 as of Mar 2017, Michael Jackson: 334,235,000 (as of Sep 2017), Elvis Presley: 318,224,000 (as of Sep 2018), Queen 274,320,000 as of Jan 2020. All figures are in CSPC (Commensurate Sales to Popularity Concept), a method which attempts to relate the different formats (albums, singles, streaming etc.). Data source: Best selling artists of all-time.
ALSO OF INTEREST
The article Who was the world's biggest music act of all time? presents an interesting interactive graphic which allows one to modify different parameters when calculating sales (e.g. value of albums versus singles). Most combinations put the Beatles on top, but when singles and album sales are both counted as one sale, Elvis Presley sometimes heads the list.
The article Is Elvis the Biggest Selling Recording Artist? - Sorting Out Records Sales Stats & RIAA Rules provides a sharp critique of the RIAA and argues strongly that Elvis Presley is several hundred million ahead of the Beatles. The authors present a convincing case in parts, but they are also connected to RCA records (Presley's main record label) and, at the same as saying we should stop arguing about who has sold the most records, insist that Elvis comes out top.
The article Did "Thriller" really sell a hundred million copies presents some interesting insights on how sales are miscounted.
The article Who was bigger: Elvis Presley or The Beatles? says that the Beatles outsold Elvis Presley in the US and then claims that:
When figuring sales of singles, EPs and albums worldwide, many
historians believe that Elvis is the best-selling artist period.
However, it gives no sources and I haven't found anything to confirm this. In fact, Baker's Biographical Dictionary of Musicians, Volume 1 mentions
The Beatles' unprecedented commercial success
