Here's some data from Billboard:
(1) Licensed to Ill was the first-ever rap album to reach #1 on the Billboard Top 200. It spent seven weeks in the top spot beginning March 7, 1987 and stayed on the charts for 73 weeks. Amazingly, there was just one Top 40 single from the record, the still ubiquitous "(You Gotta) Fight For Your Right to Party"--and it only reached #7.
Then again, the Beastie Boys never really were much of a singles band at any time in their career. Instead fans dug deeper for songs like "Girls," "Pass the Mic" and "No Sleep Til Brooklyn." The biggest hit singles (as far as the Billboard Hot 100 is concerned) were:
1. "(You Gotta) Fight For Your Right (To Party!)" - 1987 - No. 7
2. "Intergalactic" - 1998 - No. 28
3. "Hey Ladies" - 1989 - No. 36
4. "Brass Monkey" - 1987 - No. 48
5. "Ch-Check It Out" - 2004 - No. 68
(2) As an album band, the Beasties were kings. Ill Communication, Hello, Nasty and To the 5 Boroughs all debuted at #1
(3) The Beastie Boys were the rarest of rap/rock/hip-hop/alt-rock hybrids. "Ch-Ch-Check It Out" was a #1 track on the Alternative Charts (their only #1 as it turns out). Meanwhile, they had two Top 40 hits on the Hot R&B/Hip-Hop Songs chart ("It's the New Style" and "Paul Revere," both in 1987). They had four songs on the Dance/Club Songs chart ("Hey Ladies" reached the highest at #15). "Hey Ladies" was also a #10 Rap hit.
(4) Since Nielsen initiated the Soundscan era in 1991, the Beastie Boys sold 20 million in the US alone. And that doesn't include proper numbers for Licensed to Ill and Paul's Boutique, the sales of which were based on estimates. For example, it's estimated that Licensed to Ill sold 9 million copies although only 5.5 million have been tallied by Soundscan.
(5) The Beastie Boys have also sold 5.9 million legal downloads. The biggest hit? "Fight For Your Right" with 746,000.
All data courtesy Billboard and Nielsen Soundscan.