I also always call. Happy is correct that, if you have an outstanding balance, you will not be able to move 100% of your credit line over to another card. I do prefer to retain all of my credit line so that there is lots of room to apply for other cards in the future.
My Chase United card comes up for its annual fee in January. I did call a few days ago to discuss cancellation. The agent told me that there is currently no retention bonus, so I was ready to cancel, but I realized that I have an outstanding balance. So I'll wait until that balance is paid in full (it's best to wait at least 2 business days after your payment date to be sure the payment has posted). In case I end up waiting until January, the phone rep told me that there is a 60 day grace period after the annual fee date to get a full refund of the annual fee.