Can you drop out of your work insurance plan at any time if your spouse's new job offers you better coverage?

Check and make sure that your spouse's employer does not require you to keep your insurance first. My employer requires that if your spouse has insurance available through their work they must get it or they will drop them from their policy.
Yes. The problems come not when you drop a plan, but when you want to sign up for a plan and it's not open enrollment or you're a new hire.
For more info see http://www.steveshorr.com/bc.group.htm and scroll down to "deleting employees from a plan"  
My ex wife has custody of our two children. She just put insurance on them from her work a few weeks ago. I just graduated college and put them on my insurance at work. Her insurance says that she can't drop the dependant children with out an "event" happening. They said I would have to go to court and have the court order me to pay support, then they would drop her coverage. I belive you can drop anytime. Does anyone know if I am right or not?
ANSWER
If the employer takes the premiums for the insurance in pre-tax dollars by using a 125 Flex Premium Only Plan, the IRS can penalize the employer for allowing employees to drop the insurance plan without an IRS qualified "event." An event is defined as a birth, a death, a marriage, a divorce, an adoption, a change of employment, a court order, a move of over 50 miles.