Ramifications of not paying off your mortgage balance

I'm in Canada and ours are a bit different, but if we have a 25 year mortgage, ours are renewed throughout that 25 years in whatever increments we chose (eg 3 year term, 5 year term).  When our term is up (the shorter period), it is just renewed at the current interest rate.  Our amortization period (ie 25 years) is set up so that at the end of that 25 years, the mortgage is paid off and there is a balance of $0.