The National Bank of Abu Dhabi NBAD, with a restriction:
Go to the Abu Dhabi Mall - branch, and deal with Mr.Mohammed. He's excellent. You usually have to cue up for some time till you get to him, but I'm very pleased with his help (and that was often): I had money stolen out of my account twice, I had wrong transfers being made and my internet-banking didn't work for weeks. He sorted it all out for me until now.
Apart from that: The service-hotline is a total waste of time - the idiots at the other end hardly speak english, and drive you mad with their stupidity.
The NBAD-Airport-branch is a piece of sh!t, might as well forget it. They can't even issue a new cheque-book without trouble.
And I haven't tried out any other banks or their branches until now.