When refinancing, don't take the first offer that comes around. Instead you should actively compare both interest rates and lenders.
Refinancing may not be that useful if you have already used up 90% or more of your home value in taking out a mortgage or any home equity loan. You won't be able to get the best rates available in the market as when you refinance a 90% LTV loan, you will probably require a loan of that value or higher. This will be quite closer to being a 100% financing option and hence mortgage refinance rates will be comparatively higher. Moreover, 100% loans are hardly available in times of mortgage market crisis.
Ask for more than just rates. Bad loan officers will tell you anything to keep you on the phone -- then change the details to suit them later. Instead, make them get real with you! Ask how long they've been in the industry. Probe them about their experience in the industry. Also, ask what their opinion is on the current market and where it's going.
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.