Refinancing to lower your actual monthly payment:
Increasing the term or lowering the rate could reduce you monthly payment. The relation  between the property value and the mortgage debt is a determining factor, providing the standard basic requirements are met.

Refinancing to get cash out:
You could refinance to get cash out without increasing your interest rate, and sometimes even lower it. The relation between the property value and the mortgage debt is a determining factor, providing the standard basic requirements are met.