I fish mostly saltwater, so I'm not sure if it would apply to other waters, but:

I generally take two rods with me, one for sinking flies and one for topwater flies. Depending on wind conditions, they may be either an 8wt and a 6 wt or two 8 wts. Sometimes I take a spinning rod as the third rod like Jeff. I use it to locate fish rather than blind casting a fly and for quick casts while on the move if I see something. I don't see any particular reason to carry 3 fly rods.