Otherwise you chances are slim but not zero. Dress smartly, be polite. Check in just before checkin closes* - but don't leave it too late or you won't get on at all, since the flight needs to be over-booked in economy to begin with.
Join the airline's frequent flyer club and do lots of flights.
*This does have its disadvantages if you are NOT upgraded, as is very likely - you'll get the last and worst seats in economy and may not be together.
have a friend with access to the pilot!
im an air traffic control officer working at london radar centre. as you know if you are flying out of london you will be in contact with atc via vhf radio. when not too busy a little mention of a friend on board often results in a mention over the cabin address system sometimes accompanied by a move upstairs or attentive service from the stewards. more drinks anyone??
I've occasionally dressed nicely and asked sweetly and not got one. A couple of times I've done nothing at all, not even asked, and been given one. I have no idea why. Do be polite to all the staff you meet, as they can kill any chances with a snap of their fingers.
You will get an upgrade if the airline NEEDS to upgrade someone (eg through overbooking) AND you look suitable (ie would fit in with the business travellers) AND there is no-one booked with a higher priority (eg frequent flyer club member) who has still to check in. Only then if you ask....