I know HSBC online banking allows money transfers internationally and you can choose whether for the sender or the recipient to pay for the transfer fees. Does anyone know if any other bank's online banking allows international transfer too?

It depends on the country ( have its own regulations on FX control) , Bank ( at which you are having account), currency value and purpose etc:

Nearly all the top international banks allow such a transfer. Bank of America, Swiss bank, Dubai national bank, and many more allow this facility.