I am going to assume that you mean romantic love, and base my opinion around that.
In which case I would say that yes, love does hurt, because it is not in human nature to do it. Humans are a cruel, uncaring and entirely self-centered race who are only in things for themselves. The "true" love spoken of in poems, stories and songs is an impossibility for humanity, because everyone puts themselves first. When people try to go against their nature, it WILL hurt, because they simple cannot do it and it is extremely frustrating when it does not yield the expected results. Love, or what is perceived as love, NEVER lasts, because it is never fully reciprocated, for you cannot know someone else's emotions or thoughts, and, unless you die at the same time as your partner, you're going to be left alone.
For love to NOT hurt, you have to have ABSOLUTE faith - an impossibility, because everyone doubts at some time or another - and/or just not care about what the other person thinks, which completely denies the point. Or you have to die before it starts to hurt. None of those are particularly nice options, in my opinion.