Our rate came down 2.125%, which ends up saving us hundreds of thousands of dollars over the course of the mortgage.
We still have the 15-year second mortgage, but I called them up and asked if they would lower the rate, and they reduced it from 9% to 6.29% without any fuss. Very nice of them.
According to the mortgage application, we didn't take any equity out of the house with the refinance--but although we paid the loan costs and escrow setup out of the loan, we get the old escrow account back into our pocket. Plus, we don't have to make a payment until the beginning of August. With all these factors together, we end up with several thousand dollars more in liquid funds--and that's a great relief to me. I am willing to pay a bit for liquidity.
Refinancing seems like a very "adult" thing to do, with a connotation of "sensible" and "settled" and even perhaps "stodgy".