Conflicts will arise when the two separate programs compete and fight over who will delete this virus or who will quarantine this bit of spam or spyware... When it comes to "real time" security software, you should only run one at a time. Sometimes other products can be installed but it's not a good idea to have the actually running in the background together.
Hope this helps.
Is there any reason to use Norton Internet and Zone Alarm security on the same computer? I have Norton Internet and Systemworks. I like the idea of identity protection with Zone Alarm. Norton works very well for me so far. Any problems running both?