The Heart of the Problem
Do you think people doubt today, not because of a problem they have in the mind, but because of the implications belief would have on their body? Our problem is not that there is only one way to God. The heart of the problem is not in the limitation of ways, but in the limitation of our autonomy. We want the freedom to either add or subtract from any given offering. 
But we have a problem with that verse. The man himself said it, and we take issue with it.
"Well, that's just too exclusive," we say. "I refuse to believe the good people from other religions don't get to go to heaven."
That's a valid argument, except that it's not God's problem, it's our problem. We fail to see that the statement is really an INCLUSIVE one. The problem probably comes from the phrasing, since it is a negative (no one comes to the father, etc.). Let's flip this around. Sure, none come to the father except through Christ. We get that, it's exclusive, but we miss that this invitation was given to EVERYONE. No matter your age, occupation, background, no matter what you've done, who you've hurt, no one is so far from God that they cannot be reconciled. He is not an exclusive God, he is inviting everyone. It's our problem that we look at his invitation and say that it's too restrictive or doesn't work right for us.
You were given the seriousness of the word of God, but you denounced that as being not gracious enough. You were brought the free grace of God, but you said that was not serious enough for you.  No matter which way God presented himself to you, you wanted something else. I am convinced that even if God came to the world in a way that completely lined up with everything that they ever wanted, the world would still reject him. "You didn't give me enough proof" but God gave them all the proof they would ever need.
We're looking at this issue from the wrong direction. You can look at Christ and exclusivity all day long and just get more and more frustrated, but instead let's look at the great invitation that Christ has given us on the cross. So many religions and faith systems, in fact I would go as far to say all of them, have some form of payment involved in the afterlife. There are things you have to do to go to heaven, sometimes you don't even know if you are going. Sometimes there is no heaven and you just keep living on and on here, paying for past deeds in future lives.
Christianity is unique. Christ came so that we ALL would have eternal life if we would simply follow him. There is nothing you have to do, nothing you have to pay, nothing you have to give in order to gain the amazingly incredible gift that Christ has given us: forgiveness.
But there is one thing that we have to give up. It is the one thing that we, as humans, do not want to give up, and that is our autonomy. Let's go all the way back to the beginning of time: Adam and Eve. They tested their autonomy, they sinned by taking their lives and futures into their own hands, and if you think about it, every single sin we commit is the sin of autonomy. It may take many forms, but at its heart, it is exactly the same thing that Adam and Eve committed.
We all want to be able to call the shots. We all want to be like God in that we choose what is good and what is evil. We've been struggling with it ever since, and Christ came so that we could shrug that off. We could get back to submission to our creator. This was his ultimate act of love for us, and he did it all for his own glory.
What is more loving: a God that lifts us up, or a God that, at great cost to himself, positions us to lift him up? We're too self-centric. Everything is about US. That's just how our culture has grown, that's how human nature has grown. What has God done for ME lately?
How has that worked out for you? What fruit have you been getting from looking out for yourself? Has that made you happy or righteous?
You can be a slave to yourself, or a slave to righteousness. There's no middle ground, and perhaps that's where we get this idea of exclusivity. The world hates black and white, and fail to see that this is a black and white issue. There are no shades of gray here. You are a slave to sin, which is death in the end, or you are a slave to righteousness, which will lead to eternal life. Yes, slavery to yourself might feel good in the here and now, I don't deny that, but do you want to live for the now or for eternity?
I know my answer.
1. Paraphrased from Ravi Zacharias. The original content can be found in his podcast here: http://www.rzim.org/let-my-people-think-broadcasts/top-five-questions-part-3-of-3/
2. Another set from Ravi: http://www.rzim.org/let-my-people-think-broadcasts/the-anatomy-of-faith-and-the-quest-for-reason-part-1-of-2/ and http://www.rzim.org/let-my-people-think-broadcasts/the-anatomy-of-faith-and-the-quest-for-reason-part-2-of-2/
3. John Piper on DesiringGod.org: http://www.desiringgod.org/blog/posts/god-loves-us-more-when-he-loves-us-for-his-glory
Image by Sonny Abesamis (CC by 2.0)