Originally Posted by Masamune∙1600
The voice is Cloud's subconscious.
To begin, note the following sequence in Lower Junon, where Cloud has an extended "conversation" with the voice while dreaming.
Here, we see the voice attempting to cause Cloud to question his warped memory of the events of the Nibelheim disaster. This would eliminate the possibility of Sephiroth, as it would certainly have been detrimental to Sephiroth's plans for Cloud to recover his memory, and strengthen his self-awareness. As Sephiroth would have wanted to destabilize and confuse Cloud (refer, obviously, to the events in the Whirlwind Maze), one can logically dismiss Sephiroth as the "voice."
Moreover, Cloud encounters the voice during the opening mission of the game. While the line was somewhat ambiguous, it took place before Sephiroth/JENOVA had begun to actively move toward Reunion and manipulate those involved.
Also note that the second time the voice appears (again early on, after falling down into the Church in the Slums), it seems to express both a concern for and a familiarity with Cloud.
Ignoring the fact that the other supposed agents of the voice were not yet active, the voice explicitly refers to memories (specifically, "skinned knees") that only Cloud himself could have.
Note what one of the aspects of Cloud says when Cloud recovers his memories and his self-awareness in the Lifestream.
Again, reference is made to "only [skinning] my knees." As this memory was a part of Cloud's self-realization, it's also apparent that the voice might even during that early scene have been trying to steer Cloud back toward reality. In any case, only Cloud (and, by extension, his subconscious) would have been aware of that.
Thus, it should be very clear that Cloud's subconscious is the mysterious voice he hears throughout most of the game.