If you're a Bible-believing Christian, how should you perceive the unsaved, whom you believe are going to hell? I think some people might respond "with pity"; however, to pity them would be premature. You could pity their present state, of living in this world as an enemy of God, but you couldn't pity them for being on the road to hell, because they can always exit that road. God says that "today is the day of salvation," II Cor 6:2, and Jesus preached that even people who came to know Him at the 11th hour would receive full salvation, Matthew 20:1-16. To view them with pity would be resigning yourself to their "fate," believing them to be "destined" to hell.
Instead, I propose that Christians should view the unsaved as they would a friend who is going to make a bad decision. Now your perception of just how bad the decision could be will be impacted, of course, by how you view hell: if you think it's "heaven lite" or temporary or just a place of mild discomfort, then you'll view the gravity of their situation differently than if you believe that the Bible says hell is a place of eternal anguish, pitch black, consisting of physical and mental torture all due to the absence of God's presence.
In either case, though, Christians should be doing much more than they already are to persuade people to make the right decision, especially if they hold the latter view of hell. If there's any decision in life that a person you know could make that could make you cry, have you cried over the unsaved? If you'd stay up all night on the phone with a suicidal friend, would you make yourself 10 minutes late for dinner to stay late and talk with an unsaved coworker? Some Christians mention their faith to a co-worker, listen to the "Sorry, I'm not interested," and move on. Is that giving up too easily? Shouldn't Christians be doing more?
My initial reaction as I pondered these thoughts was to think that outright panic was justified; that would be the correlation to how I would act if I saw my brother about to jump off a bridge. Why shouldn't Christians be like that towards the unsaved? However, different reactions may be in order based on the imminence of the danger - my response to my brother standing on the ledge of a bridge would be different than my response to my brother taking up a lifestyle of chain-smoking. But is that adjustment for immediacy counteracted by the magnitude of the danger? My brother's plans to travel through western Pakistan in a red, white, and blue Uncle Same costume this summer would be as near as if he was contemplating going into business with a Nigerian prince, but one involves losing his money and the other losing his life - my attempts to persuade him that he's making a bad decision would certainly be greater in the case of the former.
Ultimately, you can debate the imminence and the extent of the danger that the unsaved face, but if you believe the Bible you can't dismiss it altogether. If you're not doing anything about the tens of thousands of unbelievers you know other than pitying them, you're giving up too easily.