It doesn't fit nearly as well as it should.
Luke 6:27-31
“But I say to you who hear, Love your enemies, do good to those who hate you, bless those who curse you, pray for those who abuse you. To one who strikes you on the cheek, offer the other also, and from one who takes away your cloak do not withhold your tunic either. Give to everyone who begs from you, and from one who takes away your goods do not demand them back. And as you wish that others would do to you, do so to them.
I've heard it said before that Christians are at their best when the times get tough. (IE: The old phrase, the tough get going.) Unfortunately we don't always live up to that. Part of the problem comes from not understanding the lessons of this passage. The focus is not on the earthly and the flesh, it's wholly upon the spiritual. You might not have a lot of money, maybe experience a good bit of sadness, etc. However, it is a part of life. If your primary concern becomes richness in this life...well...enjoy your reward.
The thing is about this passage that most miss is this is how Christians should handle their greatest duty. That is the duty to share the Father, Son, and Holy Spirit aka the gospel.
We all are most comfortable going to a place where folks agree pretty heartily with us. Take a look at any forum to see this in a microcosm. You have entire communities devoted to one way of thinking (or denomination) and then on others you have little sections that eventually need to be carved out so that like minds can come together. Notice in the above that these are all things that won't kill you or deeply wound you (unless you let them). When you start talking/preaching/espousing religion, some folks aren't going to like it. That's just a fact of life, you've probably run up against it by some point at this time. How we should handle this is outlined by Christ. Turn the other cheek; a slap, while insulting, doesn't kill you. If someone persecutes/absuses (as the ESV says here) you, keep on moving. I hear that p-word thrown around a bit. If someone vehemently disagreeing with you on a forum or in life is the worst persecution you'll see, count yourself blessed!
Now on the other hand I think some want to take this verse in the opposite direction that Christians must remain second class citizens and lovers of abuse. If one thinks that way, then the point is clearly missed. This passage does not, for instance, address extreme circumstances where true hurt or even death is involved. To take this verse and extend it onward is outside the Bible. Stick with context.
Something that goes unnoticed in many Christian circles is Christ just gave us the best way to make our case and plant that seed. To use an overused phrase, the most powerful ground is the moral high ground. When someone slaps you (insults you), immediately turning into a tit-for-tat match won't get you anywhere. Contrary to how you may feel, when two posters (as an example) argue and it begins to break down, most ignore both. You're just not going to make a case by persecuting the persecutor back, period. It's the old phrase your mother (and some of you mothers out there) have probably used: kill 'em with kindness. Have you ever noticed how you can totally change that counter clerk's attitude by issuing a smile and using polite language? That type of love is not just limited to places of commerce.
The type of love is Christian, because no matter how rude that person is, if you remain calm and collected, the Holy Spirit will work through you and the words you use may just very well stick with that person until the day when he or she sees the light. If those words are insults, do you think they'll stick with the person? Remember, we are to know the fruit but God will handle the chaff.