It stayed on Billboard's top 200 album chart until April 23, 1988, when it dropped off the charts for good. It had been there for 723 weeks, the longest of any album, ever. The second longest chart stay was somewhere around 9 and 1/2 years, for Johnny Mathis' Greatest Hits.
After this, Billboard changed the format so that once an album dropped off, it could not return. Otherwise, DSotM would still be accumulating weeks.
Dark Side of the Moon on the USA Top 200 Charts: Debuts on 17 March 1973 and stays until 19 October 1974 (84 weeks) but falls off. Appears on the charts again on 12 April 1975 and stays until 6 March 1976 (lost 24 weeks, but stays for 48 weeks more). Back on charts again on 18 December 1976 and stays for a record 11 years until 23 April 1988 (lost 40 weeks but gained 591 weeks). On USA charts for a grand total of 723 weeks: