I once flew Sydney to Barbados. Sydney to Singapore. Get off the plane for refueling, have to dump all of your bottled water etc because they make you g back through security onto the same plane you just got off (pretty sure it was even the same seat but they wouldn't let you leave anything on board). Singapore to Heathrow. Bus to Gatwick. Gatwick to Bridgetown. I think it was about 43 hours of travelling. Maybe more.
A couple of weeks before that I did Heathrow to Honolulu via San Francisco(with a 45 min connection, which I missed).
All of these were in economy and I don't really sleep much on planes. Great fun.
I realise they are not technically direct but if we are talking ridiculous flights then it probably deserves a mention.