I'm starting an online poker site and need to find a reliable bank to
hold my money.  I'm looking for an account in a country with excellent
privacy laws where my identity can not be obtained.

I'd like something that doesn't cost a small fortune to setup.  Some
of the accounts I've looked at have a $30 monthly charge or a $500
setup fee.  I'd like something more reasonable.

I would look at the free zone in Dominican Republic, They have a tax
haven for overseas business for a period of 20 years, and a bunch of
privacy laws,

There is also great site with binded manuals on offshore tax havens
for businesses and how to keep your finances private,

Goto http://www.edenpress.com/

There are very few true offshore tax havens left in this world.  And
when you are talking about offshore gambling, which is illegal in the
U.S., it is extremely unlikely that any offshore bank, no matter which
country it is located in, will shield you should authorities really
want to get at you.

Even the notoriously secretive Swiss banks routinely cooperate with US
authorities and those in banana republics such as the Dominican
Republic, though they talk a good game, generally buckle under the
pressures of a US dominated banking system and release whatever
information the US government demands of them.

Since your goal of true anonymous banking is probably not achievable
in countries with banking systems in which your funds would be safe,
you'd be better off setting up an account in one of the traditional
Isle of Mann et. al. banks.  There are generally no start-up fees,
though you must consider the fees involved for transfer of money into
and out of your account.  With no bank can you avoid those transfer
fees.

You can use this 2 great articles wrote by the cheif of brikers of a forex company:

http://ezinearticles.com/?A-Guide-to-Swiss-Banking---Part-1&id=105486
http://ezinearticles.com/?A-Guide-to-Swiss-Banking---Part-2&id=106955

Clarification needed for the answer: how your money will be transfered
to this bank account?...(check, wire money transfer, from Paypal or
alike?)

I use Neteller as a central source to hold my online gambling money.
Check out some online gambling forums and you will see most people use
this site - it is very reliable.

You can setup bank accounts in most OECD countries free of charge, and
many offer deposit accounts with no monthly fees. You will be expected
to provide adequate documentation as to your identity when opening any
bank account - to prevent money laundering.

In more tax-friendly countries you can avoid this by going through a
local lawyer or trustee, who will open a bank account acting on your
behalf. They will sign the bank account opening documentation in their
name stating that they know the beneficial owner of the assets in
question, and that the funds are not the proceeds of any criminal
activity. Lawyers are legally bound by professional secrecy not to
reveal the name of their clients, and trustees may likewise be bound
or unaware of the true owner of the assets in question. Basically you
are using perfectly legal maneuver to distance yourself from your
assets. Use enough intermediaries and you can achieve good anonymity,
but it does not come cheap. Other cheaper options are available
including numbered Austrian bank accounts, off-shore companies with
bearer shares, etc. but are beyond the scope of this article.

When setting up your online poker site, make sure to have it operating
from and preferably incorporated in a country where online gambling is
legal. MoneyBookers who are based in the UK, and registered as a
European Union money transfer agent may be able to assist you in
receiving online payments for your online gambling business. Most
credit card payment processor will decline such business.