List is easy - almost all banks in a western world, which provide private banking.
What is a problem with openning account remotely with this banks?
To become Private banking client, you have to have a relationship with the bank first.
Sometimes, there are a bank which are willing to aquire you as a new private banking client remotely, but amount which you have to hold with them is higher 7 digits or lower 8 digits. If you have this money, you can hire︀ a private jet and fly by using VIP terminals where conditions for usual travellers are︁ "non officialy waved".. So you can open bank account in person.