Almost always yes. State laws differ, but even if your state insurance laws don't require your spouse to be listed on your car insurance policy, your insurer may require it. Most insurance companies require policyholders to list all licensed household members on their policy since these people will normally have access to your vehicles and will probably drive the cars on the policy on a frequent basis.
In some states, if you don't tell your insurance company about all of the drivers in your household, it can be deemed misrepresentation, a form of fraud. The state laws extend liability to household members, so insurance companies have to ask and extend coverage to them too.
If you don't want your spouse on your policy, you may be able to have him or her excluded from the policy, if state laws and your insurance company's guidelines allow. Keep in mind though if you exclude your spouse and he or she does drive your car and gets into an accident, your policy's coverage will not be extended to him or her in any way.
If you do exclude your spouse, none of the coverages under your car insurance would extend to him or her. So even in an emergency situation, he/she should not drive your car if you exclude your spouse from your policy.
If you don't want to exclude your spouse, then he or she will need to be on the policy normally. If your spouse has a car and it is on a different policy, then putting both your vehicles on the same auto insurance policy could save you money with a multi-car policy.