I'm going to assume that you're referring to an insurance plan provided through an employer. I'm also going to assume that the insurance plan(s) in question must comply with 125B regulations and any medical premium contributions by the employee are made via a pre-tax payroll deduction.
As long as the two parties are married and legal dependents of one another, one spouse may carry the other as a dependent. The only time an employee can change which medical Plan he/she carries (single, family, etc) is during Open Enrollment - that is, the once-a-year period of time the employer schedules during which employees can make changes to their benefit elections, typically on a "no questions asked" basis.
The other time an employee can make changes is within 30 days of a "qualifying event" and divorce would certainly be one of those. An employee who fails to notify their employer that their spouse is no longer a legal dependent and is no longer eligible for insurance coverage could find him/herself terminated for fraud - or even pursued (criminally and civilly) for repayment of premiums and paid claims depending on the circumstances.
Tammy - not to detract from Beth but just as an FYI - if the insurance plan is NOT subject to Section 125 then the spouse can be taken off the plan at any time the insurance plan document will permit; it is not restricted to open enrollment and qualifying events unless the plan document has that restriction. The law would not apply in that case; only the plan document.
If your portion of the premium is taken out of your paycheck pre-tax or if you have the option of taking it pre-tax, then it is subject to Section 125. If it is taken post tax and you do not have the option of doing it any other way, it is not subject to Section 125.
Read my responses to mblackirish in a similar post elsewhere on this forum.