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.
It's better to follow the 2% Rule which suggests that you can enjoy the benefits of a home refinance if your mortgage refinance rate is 2% lower than that on your current loan. The interest savings will help you recoup the costs you've paid for the new loan provided you stay in the property for a certain period of time (break-even period). However, there are no-cost as well as low-cost refinance loans wherein the costs are included into the loan. But you can expect comparatively higher rates on such loans. Moreover, these loans are limited when the market is in a credit crunch.
When it comes to lowering your rates you will need to weight the benefits of having a lower rate vs. paying points up front. You may end up paying a lot more depending on your choice and how long you plan on keeping your mortgage.
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.