There is no such thing as an absolute answer to this question, so the answer is no, not all Christians think this. However, I will answer this in the terms of the majority of the Christian population.
Christianity is, by nature, a missionary faith, and Christians do generally believe that being Christian is the only way to salvation. That being said, this does not mean that all Christians, or even a majority of Christians will try to convert you to their beliefs. From my experience, I would say that the majority of Christians are very respectful of other religions (respect of the lack thereof being less common, but certainly still prevalent) and do not try to force their beliefs upon me.
I think that some people who have responded to this thread have failed to recognize the disconnect between thinking that all people would be better off were they Christian and actually trying to convert people. Thinking that all people should be Christian does not equal acting upon it.
In summary, I would have to say that, from my personal experiences and general knowledge of the religion, most Christians do think that everyone should be Christian, whether they act upon that thought or not.