The Wikipedia 'Far East' entry linked by Gavin C reads as follows:
"The Far East is an English term mostly describing East Asia (including North East Asia), SOUTH EAST ASIA, and the Russian Far East with South Asia sometimes included for economic and cultural reasons."
The capital letters used are my own. But it does clarify that even Wikipedia considers South East Asia to be a constituent part of the region we refer to as the Far East. Interesting discussion point, anyway. I've certainly always thought of Singapore as being part of both South East Asia AND the Far East.