arjunmenon By curvature, do you mean the fret board, the back of the neck or the relief caused by string tension?
Bane I assume you mean the cross-sectional curve of the fret- or fingerboard. I don't think it matters much, older instruments mostly have flat fretboards (classical guitars etc) whereas new (acoustic, electric etc) have a curved fretboards. It only changes the feel of the neck and i think the slight curvature has simply become popular over the years. One reason that may be responsible though (and i am so sucking this out of my thumb) is that curving the fretboard (and obviously the nut and bridge) increases the distance between the string but not when viewed from the top. That way all strings fit on a narrower fretboard but arent actually closer to eachother (magic), and this reduced neck size is what modern guitarists (especially those with short fingers ?) prefer.
AlanRatcliffe He means the fingerboard radius. Quite simply Heath, because it's more comfortable for the fretting hand. The narrower the neck, the more curve becomes important.
Bane Haha well here is a sketch trying to explain what i said. that was fun. notice how the red lines have the same length, but the blue one on the right is much shorter than the one on the left. Anyway that is my hypothesis, feel free to laugh at it :D
lightspeedchili i find it a shedload easier to bar chords on a neck with a bit of radius on it, dunno if thats intentional or not
