As we no longer have quite the same stiff upper lip and rolled umbrellas to hold ourselves upright, the best way is to find a spot so that you can lean against the glass panel or a window to your side, like the woman on the left:
However, when maximum tiredness takes over you cannot totally rely on the glass to fully support you and give you any dignity:
Leaning backwards and onto the ledge behind is quite a good gambit. However, you may well get a sore neck/back when you wake. Note how her arm provides additional support:
And if you are going to go for the most risky position - upright, with no ledge, window or panel next to you - try to sit next to someone holding a scary looking plant. That way you'll be woken by the spiky leaves way before knocking into the person carrying it.
Have a search through the blog if you want to check out the many occasions when I've fallen asleep and luckily the "Tube Fairies" have automatically woken me up at the right stop. Another tip for not missing your stop and waking up at Heathrow (yes I've done this) is to set your mobile phone alarm to wake you up at roughly the time it takes you to get home, alternatively wear a big badge or a sign round your neck saying "Wake me up at XXXX station", although sadists would probably let you sleep on until the end of the line!