No, not really. They rarely work out, and here's why: a relationship is about spending time with another person, getting to know him and seeing him in different kinds of real-life situations. For that, you really need to be face to face.
Yes, you can get to know someone over the phone or internet, but only to a point. Think of it as the difference between an original document and a fax; one is real, the other is a representation -- a facsimile -- of the real thing, and not nearly as defined or true. In the virtual world, we have more control over our words and actions. We can show our best face more often, and, while there's nothing wrong with that, it doesn't paint a completely accurate picture of who we are.
In the real world, we make mistakes. We say and do the wrong things sometimes. Our missteps make us human and real, and everyone wants a partner who is real. You will never get a 100% real view of another person through electronic communication, no matter how often you talk or how honest you are with each other. It's just not possible.
Don't underestimate the physical aspect of the relationship, either. You can type OMG I wanna kiss you soooo much xoxoxoxox a zillion times but it will never have the power of one real-life kiss. Ditto touch, ditto sex. Physical contact is crucial; Skype and IM are great, but they make a poor foundation for a solid, healthy bond.
As always, there are exceptions. If you're in a face-to-face relationship first and are then separated by circumstances (military, school, mission to Jupiter), the odds are much higher that you can pull off the long-distance thing, at least for a while. Some couples having difficulties can also benefit from a temporary separation. I think the longer that you've been together in person, the longer you can withstand being apart.
No relationship will survive forever without adequate face time, though. Like a plant that doesn't get watered often enough, a long-distance romance without a physical, in-the-same-zip-code aspect will eventually wither and die.