Divorce laws are set by the states, so different states have different rules. But in general, the principle is that any assets acquired during a marriage are split 50/50 in a divorce. So for example, if you had $100,000 in a retirement fund when you got married, and during the marriage this grew to $150,000, then in a divorce you would keep the original $100,000 and half of the increase, and your spouse would get the other half of the increase. That is, you would get $125,000 and your spouse would get $25,000.
Of course I'm just using one asset here as an example. In real life you presumably have many assets and possibly many debts. This all has to be added up and treated as a whole. Courts are generally realistic about this and don't say that every asset must be divided in half. Like if during the marriage you acquired two cars each worth $20,000, the court would likely say that one of you gets one car and the other gets the other car, not that you have to cut both cars in half or sell both cars and split the money.
This rule is generally applied regardless of the relative income of the parties. In the common case where the husband has a job and the wife stays home to take care of the house and the children, she might contribute $0 of cash, but it is assumed that her efforts contribute half of the family's "well-being". As another poster on here said, by taking care of the children she is saving the family child-care expenses, by cooking meals at home she is saving the cost of eating out. She may be contributing in less tangible ways, like running errands to allow him to concentrate on work or providing moral support and encouragement. (Of course it's possible for it to be the other way around, for the wife to have a paying job and the husband to stay home, but in real life that's much less common.)
Of course it's difficult to compare the value of what one person contributes by having a job to what another contributes by taking care of the home. That's why the law generally calls for a simple 50/50 split. No doubt in some marriages one person contributes far more than the other. Maybe this is part of why they're getting divorced.
None of this is hard-and-fast rules. Couples can generally negotiate any division of property that they think is fair, and unless the court thinks that one of them has been tricked or brow-beaten into accepting an unfair settlement, the court will usually honor such an agreement. Or the court may say that the circumstances call for some other division of property. I was briefly married to a woman with a physical handicap who divorced me. My lawyer told me that if she wasn't handicapped, our marriage was so short -- less than a year -- that she would have gotten nothing, but even though she initiated the divorce, her handicap made her more sympathetic so that I ended up being stuck with a debt she had brought into the marriage as well as having to pay alimony.
I don't doubt that some number of people are cautious about getting married for fear of what the spouse would get in a divorce settlement, especially people who have a lot of money. I'm not aware of any surveys that would say how many, and even if you tried to take such a survey, it could be hard for a person to say just why they didn't marry in any particular case. I mean, if someone says "I will never marry because I don't want someone to get half my money in a divorce" and who sticks to that, okay, simple case. But in real life there are surely people who say, "I didn't marry Bob because I started to worry that he just wanted me for my money". Money there is part of the issue, but such a statement indicates she might have been willing to marry him, even with the risk of losing money in a divorce, if she had been convinced that he truly loved her. That is, money is just part of the issue, a symptom.