Lobbying clearly does have some effect on policy decisions, but just how effective it is remains a topic of considerable debate in the political science community. Studies of lobbying often conflict as to whether lobbying has a small or large effect on the decisions of politicians. Complex mathematical modeling is often employed to try to tease out the effects of lobbying over other confounding factors. I've linked a few recently-published papers that try assess which lobbying organizations are successful and why.
Part of the problem is that there are many different types of lobbying, and some may be more effective than others. Some lobbyists simply make donations to campaign funds. Some actually sit down with members of Congress to discuss matters of policy. Many policy think-tanks (particularly those with an explicit political agenda) are arguably engaged in lobbying. One method of lobbying that is believed to be among the most powerful is also one of the subtlest: The revolving door, in which policymakers are often hired later by the industries they previously regulated---and very likely only offered good jobs if they regulated in a way that those industries liked.
Lobbying is often compared to bribery, in which money is explicitly exchanged in return for desired policy; but this is illegal almost everywhere. Direct lobbying can sometimes take a similar form, but it is vitally important, at least under the law, whether the money is contingent upon the policy. You can give money to politicians and ask them to make your policy; but you cannot give money to politicians on the condition that they make your policy. This is a subtle distinction, and may not be enough to really root out corruption in the system; but it is a distinction that many countries hold quite firm upon.
What we do know is that certain special interests have managed to capture significant portions of the policy process, and most likely did so through some form of lobbying.
This term is often abused, so it's important to understand what a special interest actually is, as political scientists use the term. A special interest is a group of individuals, much smaller than the population as a whole, who have a strong interest in a particular policy that most of the population does not have a strong interest in.
For example, oil companies are a special interest; most people are not employees or owners of oil companies. Beef ranchers are a special interest; most people are not beef ranchers. Software companies are a special interest; most people do not work for software companies. Being a special interest is not inherently bad, but because they have a stronger incentive to try to influence policy, special interests can often distort policy decisions toward their own interests rather than those of the nation as a whole.
Some things that are widely considered special interests plainly are not. Women, for example, are definitely not a special interest; they are in fact the majority of the population. Racial minorities are a large enough group (especially collectively) that they are clearly not a special interest. Indeed, there is reason to believe that women and racial minorities are strongly underrepresented in our political system, and this may be in part because they are not special interests. Special interests tend to be overrepresented.
Groups that organize explicitly for political action are also not special interests, unless they have some pre-existing self-interest in the outcome of the policy. For example, environmentalists are not a special interest, because their goal is to make policy that will (at least in their view) improve society as a whole. Solar power companies are a special interest, because they might stand to gain from certain policies even if society as a whole does not.
Some cases are ambiguous; unions representing teachers or truck drivers could be considered a special interest, but they represent a large enough portion of the population that they arguably are not. Gun owners could be considered a special interest, but they also comprise a large number of people and they are defined in part by their policy attitudes, not simply by some incidental factor.
It is generally recognized by political scientists that lobbying is most effective when conducted by special interests, because they have a strong incentive to put pressure on legislators that the general population does not.
Suppose for example that a policy would cost each person in America $1, and thereby raise profits for some particular industry by $200 million. This is a terrible idea; it's taking over $300 million to pay $200 million. But how hard is the average American going to work in order to save that $1? Not very. Meanwhile, executives in that industry are probably going to work quite hard indeed to get their piece of that $200 million, which even in a relatively competitive industry could be $20 million just for them. It is the very fact that they are a small number of people that gives them their advantage. So, they donate say $5 million each to key members of Congress, and wine and dine them to talk about how great this policy would be. If it works, they still profit $15 million. Meanwhile, most Americans are not going to spend even $100 to wine and dine a member of Congress just to save that $1 for themselves. Maybe a few would do it out of a concern for the $300 million lost by Americans as a whole, but that requires a level of dedication and altruism that can be hard to come by. Even then, where are they supposed to come up with the $5 million donation?
