I've known a few people for whom the third time was the charm, but I think it depends on the root cause of the failure of the marriage.

I have a good friend whose first marriage was when she was still in her teens. Her husband turned out to be gay and had only married her because his parents said they'd disinherit him if he didn't marry. The marriage was never consummated. Her second husband came home one day and said God had told him to go out and preach the gospel (and she and their 18-month old daughter weren't invited). She didn't hear from him again for over two years when he showed up on the doorstep with his pregnant girlfriend.

Her third husband adored her and she him. He was a great father to her daughter, too. They were together until he died. (It was his third marriage as well.)

So, my friend's first mistake was due to being young and ignorant. Her second mistake was marrying someone while still reeling from losing her mother and surviving a horrific accident and not in a good position to judge character. The third time, she knew a good guy when she met him because she had a basis for comparison.

Her third husband's first two marriages broke up because he was a rock musician who traveled all the time and his wives stayed home. Not long after he married my friend, he switched to session work and local gigs.

Other people break up because someone cheated or because they married for money and the money disappeared, or because they love being in love and can't handle the transition to a mature relationship. These are the folks who should be especially wary.