I am surprised I have not read at any of the previous answer this, which I consider the most crucial aspect :
I use structs when I want a type with no identity. For example a 3D point:
public struct ThreeDimensionalPoint
{
    public readonly int X, Y, Z;
    public ThreeDimensionalPoint(int x, int y, int z)
    {
        this.X = x;
        this.Y = y;
        this.Z = z;
    }
    public override string ToString()
    {
        return "(X=" + this.X + ", Y=" + this.Y + ", Z=" + this.Z + ")";
    }
    public override int GetHashCode()
    {
        return (this.X + 2) ^ (this.Y + 2) ^ (this.Z + 2);
    }
    public override bool Equals(object obj)
    {
        if (!(obj is ThreeDimensionalPoint))
            throw new ArgumentException();
        ThreeDimensionalPoint other = (ThreeDimensionalPoint)obj;
        return this == other;
    }
    public static bool operator ==(ThreeDimensionalPoint p1, ThreeDimensionalPoint p2)
    {
        return p1.X == p2.X && p1.Y == p2.Y && p1.Z == p2.Z;
    }
    public static bool operator !=(ThreeDimensionalPoint p1, ThreeDimensionalPoint p2)
    {
        return !(p1 == p2);
    }
}
If you have two instances of this struct you don't care if they are a single piece of data in memory or two. You just care about the value(s) they hold.