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Because all 50 states recognize no-fault divorce, it's pretty much impossible for a spouse who does not want a divorce to prevent one from happening. You can slow the process down by contesting it, but it will eventually go through anyway.
Contesting Grounds
If your spouse files for divorce on fault grounds, and you contest them, she must establish to the satisfaction of the court that you did what she's accusing you of doing, such as adultery or cruelty. If she can't prove this to the court, the judge will deny the divorce, but she can then refile on no-fault grounds if she's determined to end your marriage. In states that require separation for a no-fault divorce, your spouse can simply leave the marital home and wait out the separation period. If your state provides for no-fault divorces on grounds such as irreconcilable differences, you can deny that your marriage has problems, but the court will most likely simply order you to attend counseling. If counseling doesn't save the marriage, the court will grant the divorce anyway.
Divorce by Default
If you refuse to participate in the divorce process, it will occur anyway, and possibly much more quickly than if you were involved. If you do nothing when you receive your spouse's petition, she can ask the court to grant the divorce by default after a statutory period of time, usually around 30 days. It's then likely that the court will award her whatever relief she asked for in her petition.