I experience the same phenomenon, but I feel ambivalent about the best way to avoid the overload/energy drain aspect of being a 'good listener.' I can be very curious about other people. If they pique my interest, I want to know their stories and their problems, and try to understand what makes them tick. I am also very empathetic, and seem to be attracted to the experience of suffering on many levels.
So, in my case, it's not that people just happen to unload their crap on me, but often that I desire and even solicit it... to a point. They have to be interesting to me, or I will excuse myself early on. If they don't have a genuine desire to solve their problems, or don't make a genuine effort to do so, or come to seem blind/ selfish/ otherwise intractably flawed with time and analysis, I will become jaded and relatively detached at one point or another. Similarly, if it becomes clear, over time, that the person is inclined to ask for my time and compassion but is not ever willing to invest any resources in my person and my needs, I will lose interest in the one way street. Yet I find it takes time to come to this realization. The differences between a person wanting friendship and support and a person wanting a relatively free source of sympathy are often surprisingly subtle.
For me, I think the biggest dilemma arises when the balance tips in such a way that I feel I am simply being drained by our association. Because, after all, I played a role in cultivating the relationship. I was interested in them. I invited their confidences. Barring an egregious lapse on their part, it feels cruel to wash my hands of them and disappear. That makes me feel like a user or a fair weather friend in turn. And generally, I am still sympathetic to their suffering and by that point in time will have developed some genuine care for them as a person. Yet once they have become a palpable drain on me, the friendship is no longer sustainable in its earlier form.
I resort to some combination of gradually increasing distance, making more pointed comments about some of the problems I observe, and guilty compensatory listening in which I am not fully invested. It is not always graceful, and I'm not sure it's completely kind, but if people are sucking the life out of you, you will usually find yourself avoiding them or distancing yourself out of basic self-preservation impulses. In a friendship, as in a romantic relationship, inertia is not a good reason to continue on in the same vein.
Having reread this, I realize I have perhaps deviated considerably from the original topic....