Stevertigo: The lines are in fact unnecessary; they aid in framing points on the board for the eye.[1] Simple dots would work as well, as in an ASCII representation of a go board. A stone placed on the board, simply represents a given identity of a point, and represents an influence toward the identity of other points in proximity.
Hence the game is really about giving an identity (black or white) to more points than the opponent.
In Chinese Rules by the way, occupied points, (point with stones) are counted along with the empty territory, to make a total to compare with that of the other player. See Scoring.
[1]
Bill: The lines are extremely important, since they connect the points. Two points are adjacent if a line connects them without going through another point. Stones are connected by the lines, as well.
Bob McGuigan: I agree with both sides of this discussion. In fact, the lines are not necessary but yes, they are extremely important. In looking at a position on the board the lines help to see good shape and balance. I've never tried playing on a board without lines but I think the lines help to see where stones really are since stones are rarely put exactly on the points.