So here is the list I’ve gathered.
HSBC Hong Kong : https://www.hsbc.com.hk/
Very easy to open, can be done in 5 minutes via the app. Provides a Unionpay ATM card and Mastercard debit card all for free.
Charles Schwab international brokerage account: https://international.schwab.com/
Not exactly a bank account but they provide a debit card and chequebook. The debit card conveniently reimburses all ATM fees worldwide. Usually requires a $100 minimum deposit to order a debit card, sometimes can be ordered without it.
MeDirect: https://www.medirect.com.mt/
Maltese bank, provides a Maltese IBAN and a free physical debit card with an EU bin number.
Banco Atlantico: ATLANTICO Europa - O Banco do amanhã. Hoje.
Portugese bank, can be opened remotely online. Cheapest plan costs 4.99 euros a month.
Santander Spain: Online account with passport – Santander
Completely free to open online, virtual card only, physical card requires a Spanish address.
Banco Sabadell: Key Account - Account for non-residents in Spain
Can be opened online, annual fee of 160 euros. Provides a physical debit card.
Bank of America: How to Open a Bank Account as an International Professional
Requires to be opened in person at a branch in the US. US address is required (could be a mailbox). No SSN or US residency required. Capital One may also open accounts for non-residents without an SSN but it also requires an in-person visit to a branch.
Credit Agricole (Britline): https://www.britline.com/
French bank, not free, fees aren’t very transparent, requires a valid reason to open, ‘regular’ visitor to France is an acceptable reason.
HSBC Australia: International Bank Account | Overseas Account - HSBC AU
Can be opened online, requires a valid reason to open, technically saying you want to save in AUD is a valid reason but the account getting approved or not is hit or miss. HSBC are planning to leave the Australian retailing banking market in the near future.
Albo: https://www.albo.com/
Mexican online neobank, can be opened via the app and a physical card can be delivered to an address in Mexico, could be opened when going there on vacation. No local documents required.
Other options: banks in Turkey like Ziraat may open an account if you visit in branch as long as you obtain a Turkish tax id which you can get online once you enter the country. It used be really easy to open an account in China as a tourist, it has gotten more difficult now but some still get luckily. Similary in Thailand but it seems to have gotten even stricter.
HSBC US and Singapore can also be opened remotely without resdiency but they require premier status in at least one country.
Banks in Russia also open account easily to tourists (T-bank, Sberbank, Raiffeisen) but that is mainly due to foreign cards not working in the country due to sanctions. Other CIS countries such as Kazakhstan. are quite lenient towards opening accounts for non-residents as well.
Georgia has become a popular option in recent years but account opening requires an in-person visit to a branch.
This list is primarily geared towards UK residents and many of these options are only available to resident of certain countries but all them include the Uk.