Is it illegal to open your spouse's mail?

Yes, it is illegal in most situations. It is a violation of United States federal law, specifically Section 1708 of the United States Code, Title 18. No individual is allowed to open the mail of anyone besides him or herself; being married does not change that fact. The only exception would be where another party has a Power of Attorney or similar legal power (for example, if you are declared incompetent, etc.).