First, in case this is for a class, it is probably best if you can be clear on what a burglary is. A burglary is what occurs when a person enters your dwelling with the intent of committing a crime. What that means is that someone who accosts you on the street and robs you is not committing a burglary. Therefore, what you need in this case is some way of deterring people from entering your house.
The most logical thing to do, outside of owning a gun, is to have an alarm system and to make it very obvious that you have such a system. Many security system companies will place a sign in your yard. You can also make sure that the sensors for the system are clearly visible so that everyone will know that you have the system.
In conjunction with a system, you should also have motion-activated lights. These will light up whenever anyone moves within a certain distance of your house. These should help to deter people who think about burglarizing your home in the night.
Finally, it also makes sense to try to organize a neighborhood watch. If many homes in your neighborhood are getting burglarized, other people might be interested in joining such a group. The police can typically help you set up a neighborhood watch.
Thus, there are options other than owning a gun.