You can do an FHA streamline mortgage refinance if you already have an FHA mortgage. (Your bank can tell you if you're not sure). I did one last year. It doesn't require an appraisal of your house, so it's OK if your house lost value. You can also roll most or all of the closing costs into the new loan, so it could be low or no cost out of pocket, however, you can't take out any more than you originally did. If you've been paying the mortgage for a few years now then you've probably paid down enough to roll most of the closing costs into it, but if it's a newer loan then you may need to pay some of the closing costs out of pocket. Some banks offer an option where the bank pays the initial closing costs, but charge you a higher interest rate on the loan. If you're planning to keep the loan for a while this might not be a good option for you.
Finally, it is *not* required that you do the streamline refi with the same bank that currently holds your mortgage. If you're seriously interested in doing it you should definitely talk to several banks. When I did mine I got three quotes and the closing costs varied by several thousand dollars among the banks.
HTH,
Brett