Do Bank Relationships Matter?

One thing I've been wondering about is personal banking relationships, and if they matter when shopping for a mortgage. I have this picture in my head of dealing with the hometown banker, and shaking hands over a mortgage at the bank where you and the family have all the accounts and the safe deposit box. That image is definitely outdated, with nationwide banks with branches all over the place, and online banks with higher savings rates. I definitely don't have all my money eggs in one basket, which helps get me higher yields and gives me a little piece of mind with the financial market in flux. But what can I do, banking wise, to improve my chances of getting a better interest rate and good service on a mortgage? Work on my credit rating, yes. Build a good sized downpayment, yes. But what IS a good banking relationship these days? What else gets you brownie points with lenders?