In the event that you are a non-US citizen married to a US citizen, your initial Green Card will have conditions on it. This essentially means that the Green Card is only valid for a period of two years. Once this two-year period is over, you will need to apply to the US government in order to have the conditions removed.
Once the US government removes the conditions on your Green Card, you are a full permanent resident. According to US Citizen and Immigration Services, you can remove conditions by either filing jointly with your spouse or filing alone under certain conditions.
This is the more traditional method of the two. Assuming 2 years have passed in your marriage and everything is going well, you merely need to file form I-751 with your spouse. Essentially, this proves to the US government that you did indeed enter the marriage in good faith, rather than simply trying to get a Green Card. Once you do this, the US government will remove the conditions.
There are many reasons why a marriage may not work out. For example, it is possible that your US spouse passed away in the two-year period between marriage and filing for permanent residency after your marriage. It is also possible for your marriage to end in divorce for a number of reasons, including battery or extreme cruelty.
Whether or not the US will accept form I-751 if you file independently depends heavily on the circumstances surrounding your situation. However, whether you file jointly or alone, it is possible to remove the conditions on your Green Card.