What is the procedure for other banks when dealing with wire transfers incoming or outgoing where a OFAC country is involved? In some cases such as Iran, Cuba and North Korea we would contact OFAC and probally reject the wire. But what about other santctioned countries such as Liberia, Western Balkans or Zimbabwe where the sanctions are not that strict? Would the wire be stopped? Would the customer be questioned for the purpose of the wire and the relationship of the parties?

In short.... that would probably be a great idea. So yes to all of the above. Also, FinCEN can grant the right for the money to change hands, even if the country is on the OFAC list. This is according to an individual from a larger bank at a seminar I attended last week (since I have not experienced it, I cannot put too much weight into it). Our bank has never run into this problem.

FinCEN can not allow transactions without authorization from OFAC. OFAC will allow wires go to even highly sanctioned countries if they are notified,but a license may or may not be needed for the transaction.
Does any other bank require customers to provide the purpose and relationship for any wire incoming or outgoing to/from OFAC sanctioned countries.

Yes, some country sanctions permit specified types of activities.

We recently had a customer request to wire funds to a bank account in the United Kingdom where the beneficiary was a person with an Iran address. Before processing it, we asked our customer the purpose of the wire (it was said to be for personal, not commercial, purposes), then contacted OFAC to determine whether sanctions would permit us to transmit the funds. Although the transaction as described was permitted by the Iran sanctions, we were advised by OFAC to obtain our customer's written statement attesting to the purpose of the wire before sending it, to cover ourselves.

Our customer ultimately didn't want to provide us with the written statement we requested, so we didn't send the wire -- but that's another story. The point here is that you should always review the country sanctions and the particulars of the transaction before making a determination to reject or block, and if there are any doubts about how to proceed discuss the situation with OFAC.