Many pieces of music written in the renaissance and baroque periods were governed by rules of counterpoint. Especially in the early forms of counterpoint (Renaissance period) one of the guidelines followed by composers was a limited range, generally not exceeding the distance of a fifth. Avoiding leger lines was a strong rule when possible.
The C-clef is also referred to as the soprano clef. In these early pieces it was most likely employed to avoid leger lines or just to better accommodate the range of notes the instrument would be playing in that particular piece. The Harvard Dictionary of Music gives an explanation (under the definition of clefs) of the very numerous different clefs used in early music, which basically amounts to the idea of avoiding leger lines.
As music history moved forward into the classical, romantic and 20th century musical periods, many things became standardized. While the alto and tenor clefs are still used for certain instruments, many of the other C-clef placements were phased out over time and musical natural selection left us with the repertory of clefs you see in our standard music literature today.
You may be able to find some more avante garde 20th century composers experimenting with things like archaic clefs but other than that i don't believe you'll find many composers today using them.