We see examples of this all the time. The Wikipedia link above has several. The most striking examples are the ones where the unintended consequences are nearly the opposite of the intended consequences. Often what happens is that the intended consequence is a short term outcome, but the long term consequences are the reverse. These results frequently show up in situations where the factors involved are just a bit more complex than we give them credit for.
On example that keeps popping up in my consciousness is labor policies in some western European countries. They pass laws meant to protect the working class, essentially making it very hard to dump an employee, either fairly or unfairly. This probably reduces the anxiety of workers, but in the long haul investors quickly figure out that there's a lot more risk in building up a workforce in these countries, and so the investment dollars go elsewhere and fewer new companies are started in these "labor protecting" countries than might have occurred otherwise. Unemployment tends to rise. This does not seem to be good for the working class in the long term.
A separate notion is the potential reduction in productivity caused by a work force that doesn't worry much about how well it is performing. BTW: I'm something of a liberal, but nevertheless respect that market-based economies, when they are working, do a better job of making use of peoples natural tendencies to respond to incentives. And, of course, conservative policies are not exempt from unintended consequences. Recent US foreign policy was intended to make Americans feel safer, but it has arguably achieved the opposite.
Another example is a story (this should have a reference, but I can't find it right now...anybody know it) about archaeologists paying a small "bounty" for fossil fragments brought in by locals. This seems like a really cool idea, right? The archaeologists get to enlist a bunch of help in their work, plus the locals get some extra money! What could be better?! Except that there was no distinction made about the size of the fragments, and so some clever locals realized that they could get more bounty by breaking the fossils in pieces. Youch. That seems pretty counter to the desired outcome.
A very simple example doesn't even involve people (well, mostly). On cold or rainy nights, we occasionally choose to contribute a bit to global climate change by using our fireplace. (Okay, even without using the fireplace, our natural-gas-burning furnace still contributes.) But while a lovely crackling blaze in the fireplace does a fair job warming the family room, it actually makes the rest of the house colder. Say what? You must be imagining it! How can a fire make something colder? It can do it by impacting other responsive elements in the larger system.
You see, the thermostat for the furnace is located in the family room. The fire warms the family room, and the thermostat does not signal the furnace to start up. But the fire really only warms the family room, while the furnace would warm the whole house. The other rooms truly do get colder. This simple demonstration of the problems that can arise when twiddling a small piece of a larger complex system (that is, a system that includes various responsive elements).
In the other cases as well, it's the unanticipated changes by responsive elements that lead to the unintended outcome. Investors change their behavior, locals game the system, etc.
Now, one potential unintended consequence of getting too caught up in unintended consequences is that policy decisions might get stuck in analysis paralysis. That can sometimes be worse than implementing a flawed policy. Instead, be alert to the ways in which the larger system might shift but have a slight bias toward action. Stir in a dollop of responsiveness on the policy side as well. But keep the deep analysis running in the background. Otherwise you may have a recipe for a series of incremental policy twiddles and responses, that give you a random walk through human behavior without achieving any desired outcomes.
Tell me your examples of unintended consequences. Good examples help us to understand how these things work, and so perhaps we can avoid bad outcomes a little more successfully in the future.