Absolutely. Although each person starts out owning all of his or her job-related income, many states allow this to be changed by an oral contract or even by a contract implied from the circumstances of how you live. These types of contracts often lead to misunderstandings during a breakup. For example, if there's no written agreement stating whether income will be shared or kept separate, one partner might falsely claim the other promised to split income 50-50. Although this can be tough to prove in court, the very fact that a lawsuit can be brought creates a huge problem. For obvious reasons, it's an especially good idea to make a written agreement if a person with a big income is living with and supporting someone with little or no income.
Example: Jon and Rose plan to buy a fixer-upper house and move in together. Jon is a carpenter; Rose is a university professor who makes nearly twice as much as Jon. Jon and Rose plan to own their home equally, so they agree in writing as follows: Rose will pay two-thirds of the mortgage, and Jon will pay one-third. Rose and Jon will equally pay for the materials to fix up the house, and Jon will contribute all the labor. Rose and Jon also agree to equally own all the property, furniture, and fixtures they buy once they move in together.