Source: Martha C. Nussbaum, "Philosophy and Literature," The Cambridge Companion to Greek and Roman Philosophy, ed. David Sedley (Cambridge: Cambridge University Press, 2003) 226.
"[Plato's] Republic x takes an even stronger stance against tragic poetry...Once again, the ethical objection raised against tragedy is that it shows good people encountering reversals in fortune and grieving as if these had great significance. Again, the unseemly behavior of the tragic hero is contrasted with the self-sufficient calm demeanor of the truly good man, who recognizes that 'nothing among human beings is worth much seriousness' (604b). Here pity is central to the analysis. Socrates points out that tragic poetry leads to fellow-feeling, and 'nourishes the element of pity in us, making it strong' (606b). This makes it more difficult, he alleges, to achieve a calm demeanor in one's own sufferings."
Plato seems to foreshadow the Stoics, who believed people should eliminate their passions. His view, at least as I read it here, differs from what we see in the Hebrew Bible, Judaism, and Christianity, which exhort people to have compassion for one another other. But there are similarities, believe it or not. I think of my quiet time in IV Maccabees a few weeks ago, and how that Hellenistic Jewish document could find examples in the Hebrew Bible of biblical heroes suppressing their passions to do the will of God: Abraham being willing to sacrifice his son, Joseph resisting Potiphar's wife, etc. I can name other examples that the author of IV Maccabees did not include: the Levites slaughtering their fellow Israelites in the golden calf scene, the Conquest, etc. In those cases, God didn't want his people to pity their fellow human beings.
On Star Trek V: The Final Frontier (which is my favorite Star Trek movie, even though critics shredded it to pieces), a fanatical Vulcan named Sybok gains followers by taking away their pain. Dr. McCoy, for example, had the burden of putting his sick father to sleep several years before. Spock felt sad because his father never accepted him. Sybok gave them release from that "pain."
But Captain Kirk didn't want to play along. He said that our pain makes us who we are. "I don't want you to take away my pain--I need my pain!," he said.
Human beings have feelings. On one hand, they are appropriate. There's nothing wrong with feeling sad for another person, since the fact that we're even thinking of someone other than ourselves is what God wants. On the other hand, passions can lead us down a wrong path if we let them control us too much. This was why Plato and the Stoics were critical of sadness, anger, and lust. They wanted a strong human being, one who was above all these base passions. I sympathize with the Stoics whenever I get a crush on a girl: I wish I didn't have that emotion dragging me down, taking my mind off more important things.
Christianity is mixed on this. The happy-clappy evangelical brand tells us that we should never feel mad or sad, since that's a sign that we're not praising God enough. At the same time, Christianity has given us examples of really emotional people: Jesus, Augustine, Spurgeon, and so on.
As far as literature is concerned, I cry a lot. The crying can be involuntary, as when I watch Desperate Housewives or Joan of Arcadia. It's a catharsis for me.