Game lengths from 2 632 713 non-handicap 19x19 games that had a score result:
The average is 253.5 moves.
Games longer than 500 moves were ignored and not included in the average.
For this one I decided to calculate game length as (length of movelist) - 2, to remove the final two passes.
I failed to take into account that under AGA rules, white must pass last - I believe this is the reason for the spikes on even game lengths.
If I ran the analysis again, this time removing all trailing passes, we would get a smoother histogram and a sliiiightly lower average.