Different banks for different reasons. Singapore is one I like. It's a strong stable jurisdiction but requires a visit and has high minimum balances. For ease of use the account in Colombia can't be beat. Still has the old school service. I have a dedicated account manager who I simply email with instructions to transfer funds and so forth. Got a personal account in Isle of Man which is good for simplicity. Multi-currency with low minimum balances. You really have to work out what is most important to you and find a bank that meets your criteria. I'm looking at Afrasia Bank in Mauritius at the moment but I've been told they aren't accepting new applications currently.
Worst experiences I had was probably Mexico and Panama. Local banks in Thailand were also particularly painful. These places haven't yet grasped the notion of an international lifestyle. They require a person to physically walk in to a branch to perform many tasks.
I went offshore because my life is offshore. I work and invest all around the world and I'm rarely in any one country for very long. Even if that isn't the case for you though, it's wise to have at least a little offshore. If everything is in one place, you aren't diversified. You have no backup should a government or legal action brought against you freeze your assets, if a bank becomes insolvent or the jurisdiction has an economic collapse for example.