154 regular season games.
It's worth noting, though, that there never actually was an asterisk. The Commissioner of Baseball at that time, Ford Frick, who was a the-good-old-days-were-always-better kind of guy, said during Maris' record season that if he broke the record, maybe it should go in the record book with an asterisk. However, The Baseball Encyclopedia, which is not owned by Major League Baseball, didn't agree, and Maris got the top spot to himself, no asterisk in sight anywhere. Nowadays the record book reads, "Most home runs in a 162-game season: Barry Bonds, 73. Most home runs in a 154-game season; Babe Ruth, 60."
It should also be noted that Ford Frick was Babe Ruth's ghost writer for newspaper articles that had the Babe's 'byline'. Certainly, that had to have something to do with Frick's insistance on the asterisk.