It could be very dangerous if he runs away to meet her. If that is a situation that is likely to happen then I would first attempt to at least arrange a meeting between them in a safe environment. Then you could meet him too. Internet relationships can be founded too much on fantasy. If you let them meet, then perhaps her fantasy image of him will be shattered by reality and she will end the relationship herself.

I might try to arrange them to meet somewhere, but with  parent supervison. I would also inform the boy that he also needs to involve his parents as well. That may be the safest bet. If the boy lives as far as a plane ride away, then you should somehow encourage your daughter to forget about the boy.

I have a 14 year old daughter myself and she pretty much eats, sleeps and lives on her computer.

I would sit there with your daughter while she is on the computer while they are talking and you ask the questions. If your daughter has nothing to hide then she should welcome the idea you are at least keeping an open mind and not just saying end this internet romance

There's no reason to force your daughter to break up with her 'internet boyfriend'. That's exactly the wrong approach to take with an adolescent. For her, the draw is less about having an online relationship and more about rebelling.
 
Open up a dialogue with her to talk about the risks and rewards of dating (on-line and off-line). You can turn this undesirable situation into a productive conversation about dating and sexuality. It's important that your daughter realizes you're looking out for her best interests.
 
You mentioned that they have never 'seen' each other. Encourage them to converse via webcams and social-networking sites. Internet relationships invite distorted realities; enabling them to trade pictures and use webcams will remove the fantasy element. Bringing the relationship out into the open lowers the likelihood that one of them will do something dangerous, like running away from home to meet the other one.
 
Although extremely difficult, the best thing you can do is to support your daughter.

Prove he really is a 17 year old boy.  Honestly, pay attention - VERY close attention - to the news.  
 
This is Grooming 101, dear.  Sexual predators do this all the time.  This exact scenario is carried out in attempt to keep her hooked, to see how deeply involved she will be (by agreeing to meet him and then willing to try again when his first attempt failed, she has proven to him that you pose no threat to him and she is lonely and easy).  
 
All the time she spends talking to him, also, lets him know her parents have placed no limits and that her parents aren't monitoring her online activities.  You've set your daughter up as bait, whether you want to believe that or not.  
 
By allowing this ridiculous "romance" to continue, you send her the clear message that you don't care if she has a relationship with an unknown stranger on the net.  You, also, send him the clear message you don't care about the safety concerns police warn parents about on a daily basis.  
 
You are the parent.  To the point, it is you NOT her who makes the decisions.  And if you are allowing her to continue a relationship online with a complete stranger, the result will be on you.  She is a teenager.  A kid.  She needs discipline (self-control, self-respect) and parental responsibility. She seems to, also, need more involvement by the two of you in her life and real life human interaction.  Please show some or she will be another statistic on the evening news.
 
I would strongly advise getting the police involved.  They do not take this kind of thing lightly.  The very fact that he has told her he tried to run away and had her agree to a meeting is enough for them to do a full investigation into his true identity.  Your daughter is in danger.  Do something about it before it is too late.

Don't EVER EVER EVER let your kid do webcam with strangers on the net! OMG!!!  That is totally right about you not knowing its a boy or not.  Don't you watch the news?  It's on all the time about teen girls from like myspace being kidnapped and r*ped by pervs that said they were teenage boys.  If your daughter can't understand why you don't want her talking to this guy, that's her problem.  I would rather my mom be my MOM and keep me from being R*PED than be my friend and let it happen.

My wife works with sexually abused kids and teens who have been raped and abused by older kids and adults. Many of the girls met their abusers online and thought they were other kids and many of the parents my wife helps are parents of girls that have disappeared because they met "boys" online.  Theres a growing industry of selling girls on the black market for prostitution in other countries and my wife is part of an organization that alerts people to things like "rapto".  Over half of the girls kidnapped met their abductor online. It is unwise for you to allow this "relationship" and to listen to anyone who tells you to let it continue and to develop into anything including sharing videos and photos. I see what my wife works with and the families destroyed by one mistake.  You don't wnat to to be one of these parents.

Involving the police, or asking your daughter if she’s watched the news lately will make her feel alienated and stereotyped, and she will be more likely to rebel, and put herself in a potentially dangerous situation.
  
I agree with the comment about breaking down the fantasy. Allow them a supervised meeting, or let them speak over a webcam. If she can hear his voice, and see him, she will likely see someone different than she pictured in her head. This will give her a reality check.
  
Bottom line: No one wants her to run away from home and meet some guy who may or may not be who he says he is. The role of a parent is to teach a child how to be an adult. Using force will not educate her on personal responsibility, or encourage her to think critically about the situation.
  
If it turns out he is who he says he is, and they hit it off in person, maybe they'll end up together. Would it really be so terrible if two teenagers met and fell in love over the internet?

I am sorry that you are getting though a hard time with your daughter. I was that kind of daughter and I left my home in Russia to come to the USA through correspondence. My mom tried to talk sense into me, too. But I insisted on my way for my inner desire for what I decided was very strong. I came to the USA and got myself in a pickle.
 
I wish you the best luck with your daughter, perhaps, she is still young and she will understand and will act mature, but you are doing all you can and you are a good mother and some kids just do not listen...
 
A link to my story below.