"Mortgage insurance" can mean any number of things. If you're referring to your homeowners coverage, yes you can; but if your mortgage still exists, the lender will put forced coverage in place (probably at a higher cost). Private mortgage insurance, or PMI, is coverage that the lender requires if you have less than 20% equity in the property. If you have or can pay down your mortgage to less than 80% of the home value, you can get this cancelled. Eliminating PMI is a high priority; it protects the lender, not you.
If you are talking about mortgage life or disability protection, yes you can cancel it; but don't do so until you have something else in place. In most cases, your mortgage amount should have been a factor included in your regular life and disability planning. Supplemental life or disability coverage is usually not as cost effective.
Financial planner, 11 years