Have you ever been in a discussion with someone, only to have another person step in to join you, and thereby interrupt or completely change your conversation? Sometimes it's not an issue, such as when you are engaged in casual chitchat, but there are other times it can be very disruptive; you have made a point to seek this person out for a specific reason, yet along comes an interloper and just that quickly, your need goes out the window.

Is this done on purpose? Usually not; I believe that the majority of people do not consciously choose to be inconsiderate. People have their own agendas, and as a very self-focused society, we look to take care of our needs without noticing what may be taking place around us. It's not necessarily about interrupting a conversation ... perhaps it's about joining in.

Still, it's frustrating, isn't it? So, as the interrupted party, how should you respond? One option is to simply move along with the change in conversation, realizing that if you are in a public place with a group of people, such as church, work or at a social event, you shouldn't have a real expectation of privacy. Another option would be to acknowledge the disruption by telling the person you were talking with that you will "follow up on the conversation later" and then either politely move along yourself, or continue with the new topic. A benefit to the second choice is that it may discreetly - and courteously - let the uninvited participant know that a boundary was crossed. You might even receive an apology for the interruption.  

If you are in real need of an undisturbed conversation with someone, it would be best to make it a private discussion, one where interruptions are not likely to happen. Keep in mind that just about any conversation can go from general to private fairly quickly; as has been said about many other things, "prevention is the best cure."