It is feasible to go for a refinance when you have built up at least 10% equity in your home (For Fannie Mae owned mortgages, the value is 5%). It is also possible for you to choose the option if your equity is less than 5%, but you may have to pay a certain amount of cash in order to make up for the difference in equity.
If there are only a few years left on your current loan, it's no use refinancing with a long term loan. You may need extra cash but with a long term loan, you'll end up paying more for the entire loan term.
Don't fall for the 0% apr unless it fits in with your master plan. A lot of brokers will try to get you locked into a low interest rate that will balloon on you in a couple of years and leave you out on the street.
Be Prepared. You'll probably be asked for more information and documentation after you submit your application, but before your loan is approved be prepared to document your income and assets. Answer any questions and fax documentation to your loan representative as soon as possible.