I have wonderd, but never asked, if any Bank will waive or lower the fee ever
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Other than the Slate that was mentioned already I can't think of any that offer no BT fee and 0% intro APR on BT's, I know Barclay has a card(Ring, I think) that offers no BT fee with an APR of like 8%.
You're probably asking about 0% APR and no balance transfer fee cards. Navy Federal CU has promotions periodically for this and also mails out targeted offers with new credit card applications. Alliant CU also offers this for new credit card accounts.
Chase Slate is the best BT card IMO.
Coastal FCU in NC has a 0 BT fee, 0% interest card for BT greater than $600, but the balance has to be paid off in 6 months. It's called the Big Ticket card.