No, you and your spouse are not required to file for bankruptcy together. However, you may both want to file for bankruptcy jointly if you and your spouse share responsibility for the debt. If you and your spouse have co-signed a debt together, this may be a debt that the two of you share. For instance, if you have bought a car together, you may both have signed for the loan.
If you live in a community property state (Arizona, California, Idaho, Louisiana, Nevada, New Mexico, Texas, Washington, or Wisconsin) or have opted in to community property arrangements in Alaska, you and your spouse are jointly responsible for debts either or both of you incurred during your marriage, even if you did not "co-sign" for them. This may impact whether or not you decide to file jointly or whether you want to file on your own.