Almost all offshore banking (read: tax havens) will open an account without you ever visiting. Think the Bahamas, Grenada, St. Lucia, St. Kitts & Nevis, et. al.
However, this does not mean they are lax in their KYC. Quite the opposite. You will have to provide a bunch of documents to authenticate your identity and then your account would be opened.
The caveat? There is a minimum, usually US$ 50,000 to start with, to open an account.