It depends on the type of financing you used to purchase the home and when. Up until recently, both FHA's MIP (Mortgage Insurance Premium) and Conventional's PMI (Private Mortgage Insurance) canceled once the loan balance reached 78% of the home's value. Somewhere in your mountain of mortgage documents there is likely an amortization schedule that shows the mortgage insurance disappearing at some point in the future.
With some private insurance you can also petition the lender to have the PMI canceled. Typically the lender will require an appraisal and for you to be in good standing on the loan. If you have at least 20% equity it will likely be canceled.
Most PMI products also have a minimum period that the insurance stays in effect for, regardless of your equity position so it is important to review your specific closing package,
Recently FHA has changed it's policy with regards to MIP and now requires it to stay in effect for the life of the loan. This has made the portfolio and conventional mortgage products far more attractive for many borrowers.
It is important to work with a mortgage professional who has access and a working knowledge to all of these available programs so that an unbiased recommendation can be made that best fits your specific goals.