In the past the decision was pretty simple, you repaired your camera. Buying a new one didn't gain you much, but today the question is more complicated.
One of the chief concerns is the landfill problem. With the advent of changing technology obsoleting equipment every 6 months, our landfills are quickly filling up with discarded electronic products and worst of all batteries. If you are concerned about this, then the answer is a little bit more clear, try to have the equipment repaired. If on the other hand you are not concerned with this, then you may consider the following questions.
First, prior to your equipment failing, were you happy with it? If so, then repairing it would be a good option. But the next question is, what is the cost of the repair? Will it be close to or exceed the cost of a new camera? In this case, you may want to consider a new camera. However not all broken cameras are repairable.
Aside from these questions there are other factors to consider as well. What will you gain with new equipment? These days it often means more resolution, but if you don't enlarge your photos much to begin with and you were content with what your current camera's resolution, then it's not much of a gain. A new camera will generally give you a larger lcd screen with better resolution as well. This does make it easier to see what you are photographing or have photographed. With a new camera you must also consider that with the higher resolution comes more consumption of hard drive space.
Depending on the types of things you like to photograph, increased functionality may or may not be useful. With DSLRs and point and shoot cameras, you may get faster auto focus, more accurate auto focus, better image stabilization, better resolution at higher ISO's, more accurate metering and faster processing time. Better resolution at higher ISO'S means you will be able to take photos at increasingly less light without noticeable loss in resolution. Better image stabilization means that you will be able to handhold better in low light.
So although there seems to be significant advantages to getting newer equipment, if the type of photography you do does not benefit from these technologies, then there is no need to purchase a new camera if repairing is an option.