If you are covered under an individual policy you should be able to drop them from the coverage at any time during the year. The termination would generally be for the first of the coming month as your insurance carrier may decline to do a retroactive termination of coverage due to the possibility of recent unreported claims. You should note though that in today's environment dropping your spouse from your individual coverage could leave your spouse uninsured until the next open enrollment period, which this year begins on November 15th for an earliest effective date of coverage of January 1, 2015. If your spouse is becoming eligible for Medicare then you will want to time the termination of the spouse's coverage to match with the effective date of their coverage under Medicare.
If you are covered under a group health insurance plan and you a having your portion of your health insurance premiums taken out of your paycheck on a pre-tax basis then your employer has a Section 125 plan in place and this restricts changes an employee can make to their enrollment status outside of the group's open enrollment period. A change of life status event as defined under IRS regulations would have to occur for you to remove your spouse from coverage outside of the open enrollment period.
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If you are covered under a group health insurance plan and you a having your portion of your health insurance premiums taken out of your paycheck on a pre-tax basis then your employer has a Section 125 plan in place and this restricts changes an employee can make to their enrollment status outside of the group's open enrollment period. A change of life status event as defined under IRS regulations would have to occur for you to remove your spouse from coverage outside of the open enrollment period.