Let's see - just from memory (so it's faulty) the artists or groups I have the most works of are:
On purpose:
Rush
Mamas and Papas
David Arkenstone
The Smiths
Bob Dylan
The Monkees
The following just happened without intent:
The Moody Blues (Just wanted one album, now have about 7 of their albums)
Yes (Just wanted Yessongs, now have something in the area of 14 to 17 of their albums)
The 5th Dimension (Again, one greatest hits I thought was enough, now have all but two of their albums)
The Byrds (Thought Greatest hits would do it, now have all but 2 or 3 of their albums)
Catherine Wheel (Was happy with one, ended up with all of them)
Petula Clark( One album begot about 10)
There's probably more, but all I can think of without looking.