Professionals photographers have a wider range of experience to draw from not just on the artistic side, but the business side as well.
They know how to avoid problems, and how to improvise when things do not go as planned. Professionals like Ben Zander generally have more and better equipment. Also, they provide backup cameras, batteries, etc.
In case something should break, low light levels, or fast action. Each piece of equipment provides more flexibility needed to photograph in more circumstances. Professionals have a system in place for everything from knowing what types of photos you want, to categorize, order, and delivery.
There is nothing worse than realizing your photographer forgot to get that 4 generation picture. In an event like a wedding, there are no second chances to capture the images. It has to be done right the first time.
Spend some time looking at different photographers' portfolios. The more you look at the better feeling you get for the style you like best. Start making a list of the types of pictures you like. Find photographers who already show work in the style you prefer. Non-professional photographers are often still exploring their style and you not likely to see a consistent look at the photos that a pro will provide.
You will also need to spend some time talking to the photographer. This can be time-consuming, but some personalities just do not work well together and you want someone who will enjoy working. Ask if you can watch a photo session with another customer. This will give you a very good idea of how the photographer interacts in different situations.
Weddings can be especially tricky trying to coordinate so many people. Make sure you are not getting a Jekyll and Hyde -great one on one but a monster in a group.