Living together is fine, but marriage is not just a piece of paper. As I have done both, I feel that marriage is much more of a commitment to a person. You can live together, but it is "easy" to just leave and not work things out. If the person won't marry you, it tells me that there is something "wrong" that they don't want to make that full commitment to you over. Yes, people do live together for years, but it does not make any future marriage better. In fact, people who live together first have the same, if not higher divorce rate as all the rest of us.
To me, marriage is more than a piece of paper. It tells the world that you are willing to make a lifetime commitment to that person.