This can be a difficult question to ask as there are two different ways of looking at this scenario (as there are every scenario).
Some believe that Christians should only date other Christians because of scriptural references. Some say it's okay for a Christian to date an unbeliever because they can use they're relationship to draw a lost soul to the Lord. So, should we or shouldn't we?
For those who believe a Christian should be able to date an unbeliever, they use the whole "Missionary Dating" excuse (as mentioned above). They believe that through this relationship, they can lead an unbeliever to the Lord through their witnessing. This could be okay if looked at this way, however, it's very rare that this actually takes place. Usually it ends up where the Christian has found themselves in un-Christian-like situations or places. Instead of the unbeliever drawing closer to the Lord, the Christian begins to stray as they pick up bad habits.
Then there's the argument, "I can't find any good single Christian people. They're all dating someone already or they're a geek." Something along those lines. Yes, sometimes people confuse kindness with weakness or geekness. But keep in mind that there are always new people becoming Christians every day. There are many current Christians whom you have not met. How can you meet them? Start attending more Christian events. Get out there in the Christian world and begin to socialize.
God already has someone for you. You and that person are on two seperate paths. At some point, God will intersect these paths. The question is, are you where you are supposed to be on that path? God cannot force you to walk that path, but he does encourage us. Some of us fear that even if we "are" on the right path, how do we know our "special" someone is where they are supposed to be to meet there? The best way to find out is to be everywhere the Lord tells you. If you havn't found the person yet, then your path wasn't meant to intersect yet.
With all explainations aside. If I had to answer the question to this blog with a simple "yes" or "no," I'd have to say "no."
I try to base all of my opinions on scripture (as we all should do). This is a sure way not to go wrong. Here's what scripture has to say:
2 cor 6:14 Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?
This tells us basically that if you mix black paint with white paint, you'll have gray paint. In other words, an unbeliever (black paint) mixed with a Christian (white paint) results in a less obediant/less faithful Christian or worse (gray paint).
As Christians, why tempt ourselves by allowing a sinful lifestyle to enter our own. Is it lust that sways us to deny scripture? Usually. Some people choose kissing and cuddling over what is right... a pair of lips over God.
If you like (have a crush on) someone, and they are not a Christian. You should be more concerned with their soul burning in Hell than how good they kiss. Your goal should be to lead them to the Lord... as a friend. Once they find the light, then date them if you must. With God in a relationship, trust me.... MANY problems that "would have" taken place will not now.
So, put hormones aside and read the Word. If you really cared for someone so much that you wanted to date or even marry them, you should care about where they end up after they die or when the rapture takes place.
Lead them to the Lord... then it will be mixing "white paint" with "white paint," leaving your paint "white" (Christian) still.