If you are able to get a lower rate that what you currently have, you can save tens of thousands of dollars over the life of your loan. Also, most lenders don't charge as many fees to refinance a mortgage and depending on how much equity you have in your home you may be able to roll the closing costs into your new loan, still have a lower balance than your original loan, a lower rate, and a lower payment.
There are literally thousands of mortgage companies all over the country. It is important that you choose a reputable one. Most reputable companies will be part of the Better Business Bureau or other community watchdog group. Good companies will also have websites that rank well on search engines such as Yahoo and Google.
Be Proactive. Your loan representative should keep in contact with you even if there isn't any action on your loan. But do your part to keep the lines of communication open as well. If you don't hear from your loan representative for a few days, pick up the phone and ask for an update. The old adage that the squeaky wheel gets the grease definitely applies in this situation.
Once you know the reason for refinancing, you should ask your mortgage specialist whether or not it would be beneficial for you to refinance at this time or whether it may be more beneficial to wait.