Actually in the UK they are still widely used. In fact they are probably the main way of making payment between individuals and/or small businesses that don't have card facilities (of which there are many). I would certainly expect my bank to accept a cheque drawn on a Japanese bank, though there might be some fees involved. But it may be different elsewhere.
I do some research and found this site for example:
http://forum.gaijinpot.com/showthread.php?114083-Cashing-a-chequeIt seems that cheques in Japan as in Germany and in many other countries not to be common. You can not compare it with the Anglo-American world. Other countries normaly do not use cheques, more precisely: bank cheques. It would also not change anything. AML and everything else also applies to bank cheques. There are even more requirements for these cheques.