If you simply stick with 3 #1 singles on Billboard's Hot 100, there are probably only a few. The Beatles probably did it on more than one album. Off the top of my head, I can recall that Michael Jackson(Bad, not Thriller), Janet Jackson(Rhythm Nation 1814), Mariah Carey(Fantasy), and Alanis Morissette also accomplished this feat.
Edit I asked an expert who said that many of Alanis Morissette's songs were not released as singles, so they did not hit #1 on Billboard. However, he also mentioned Saturday Night Fever Soundtrack, Bee Gee's "Spirit Having Flown", and an Milli Vanilli album .