We Just Don't Get Along
Most states only require that you tell the court in your petition or complaint that you and your spouse are incompatible. Some states hang fancy terms on this concept – in New York, your marriage is "irretrievably broken," whereas in Illinois, you and your spouse have "irreconcilable differences." By any name, you just don't want to be married anymore, and this is usually good enough for the court to end your marriage.
We've Lived Apart for a Long Time
In some states, no-fault divorce is more complicated. For example, in Maryland and North Carolina, you must demonstrate that your marriage is over by living apart for a full year before you can file. In Illinois, you can say you've got irreconcilable differences, but you must still live separately for a while as well.
"Pure" No-Fault States
Most states also recognize some fault grounds for divorce, but 15 do not -- including California and Florida. In these jurisdictions, you have no choice but to file for divorce on blameless grounds.