The answer to this question necessitates a clarification of what types of 'answers' science either illuminates or neglects. Science cannot and does not seek to answer questions posing "why", but rather "how", "when", "where", and "who" (think forensics). Science does not impose a value judgment on the nature of the world; it seeks to identify it's truths. Due to the fact that many scientific findings have elicited tremendous emotion, controversy, and often hatred throughout history, it has become increasingly common of late to judge the scientific process from a moral standpoint, and to question its ability to answer moral questions. Assuming this debate title is referring to the aforementioned questions that CAN be answered by science, the following factors must thus be taken into account as well.
In defining the role of science in understanding the universe around us, it must first be made clear what exactly science does. "Science" itself describes not only the systematic and empirical cognitive process of establishing an approach to the investigation of our physical reality, but also the action of testing and implementing such methodologies into practical use. The very nature of the scientific process serves to eliminate personal and cultural biases, often against the human tendency to bestow his or her desired outcome upon the process. Reemphasizing the nature of the questions answerable by science, answers are often misinterpreted to carry greater or less value to the search for truth than reality dictates.
A somewhat paradoxical and often frustrating truth of the scientific process is that for every question answered, dozens more questions often emerge. The process is further complicated by the ease at which experimental results are nullified, as compared to the immense difficulty of validating experimental results as 'truth'. Decades of work on a single concept could be instantly wasted by a single contradictory result, or that single concept could go on for centuries as nothing more, never attaining 'fact' or even 'theory' status.
The plethora of unending questions revealed by science at every turn is a reflection of the immense complexity of the universe and of the potential for human knowledge, not of the futility of the scientific method. This very document turned one question into several in an attempt to clarify an issue of great complexity. Likewise, the investigation of our universe as employed by scientific techniques continues to unveil complexity. This is not to say that nothing is "knowable"; most of what science has uncovered provides solid understanding, even if individual elements of that larger understanding change over time as more is unveiled. If there is one concrete 'truth' that the dynamic process of science has revealed to us, it is that complexity and change are the true nature of reality; in an ever-changing world, 'answers' are rarely fixed. Science has proved this, not rendered itself obsolete because of it.