In the United States, as of November 2016, the song "Hallelujah", written by Leonard Cohen, has seen 8 different versions enter the Billboard Hot 100, with 3 of those reaching the Top 40. I'm not sure whether this is the U.S. record for this particular feat, or whether any additional versions of the song have charted since then.
On edit, Leonard Cohen's original version, recorded in 1984, hit the chart on Dec. 3, 2016, shortly after his death, at no. 59 for one week. So that means that as of that week, there have been 9 versions to hit the Hot 100.