As little as possible.......

Kindle (and possibly a new book from the airside shops), bottle of water, pashmina, some nibbles if its a long flight, one of those mini moisturisers you get in beauty gifts with purchase, passport, credit cards, camera...

I used to carry half a suitcase with me - but eventually realised that all I ever used from this huge bag was my book and drink/ nibbles, so i cut back to just that... everything else is in the hold baggage

On long flights I also have pop in a pair of clean knickers and a clean T shirt - just in case the hold baggage doesn't show..... so at least I can have something clean to wear while I sort out the problem...