For most people of normal activity level a general, supportive shoe that fits well will work just fine, regardless of whether they are biking, running, playing tennis or doing aerobics.
Specialized shoes really start to make a noticeable impact for individuals who are avid participants in a particular sport, have problems with their feet or who over- or under-pronate. These individuals often benefit from a specialized shoe. For over- or under-pronators (meaning you tend to land to the extreme outside or inside of your foot when walking or running), it is best to choose a shoe that offers more arch support and stabilization.
But, how do you know what shoe is best for you? The answer: It is really just a process of trial and error. Sales professionals at the shoe stores vary widely in their knowledge of shoes and of feet. Their time, experience and training may be able to help you identify a shoe that will be good for you, and they may be able to recognize certain types of issues by looking at the wear pattern on an old shoe.
Some shoe sales persons, however, specialize in making and fitting orthotics, or inserts in shoes, and they are knowledgeable and can be very helpful in helping you find a good athletic shoe to address specific issues.
But, honestly, for most individuals finding the right shoe for you is simply personal preference. The good news is that regardless if you choose the “wrong” shoe type for you, it is very unlikely to cause injury, although you may be disappointed by the hole left in your wallet.