Growing up as a civil aviation nut I absolutely adored the Landor scheme, particularly the insignia on the tail and the bold red arrow. Looking at them now I still feel a bit nostalgic. I think the insignia really represented something quintessentially British - the monarchy. The red arrow looks entirely too brash and unrefined in that 80s sort of way now, but it was a good livery.
The world tail fins had some really lovely designs - the Chatham Rose comes immediately to mind. Too bad they scrapped the whole thing instead of keeping some of the designs, which I think also encapsulated BA's having one of the most far-reaching destination networks world-wide.
I like the current livery very much - the softness of the curves of the 'swoosh' (surely there's a name for that logo?) conveys motion and speed, and the transition of colours is very nicely done. The tail fin design of the Union Jack waving in the wind - you can't really get any closer to the idea of 'flag carrier' than that (depsite what the Bearded one would have to say about that).
I can't wait to see what they might come up with for the next one. But let's hope the next generation F will come first with real improvements!