We know they are collecting this data as they have shared a number of posters with stats from the Alpha and Beta.

At the minimum, we should be able to have access to our current characters progression in each of the guilds. As well as the gold total. I also think it would be nice to have the locations travelled to and the time spend at each location in a session.

But it does not have to stop there, there are a number of other interesting stats:
Most player kills
Most skeleton kills
Most chests found in a crew
Most treasure earned
Most treasure lost (dug up but not cashed in by crew)
Most deaths
Most time spent drunk
Best accuracy
Worst accuracy
Longest distance covered swimming
Longest time spent in battles
Most canons reloaded
The most ship hits with canons
Most people hit with canons (for those lucky shots)
Most cumulative distance fallen, for those in the crows nest drinking grog!
Most treasure chests found in a row
Most times spewing up from drinking too much grog!
Most chests stolen from other crews.
Longest fall to death.
Killed most by skeletons.
Best K.D. ratio.
Most stuff stolen from other crews.
Most time spent at the wheel. (Top helmsman)
Biggest single treasure reward.
Most time spent searching a treasure.
Most treasures stolen from other ships.
Most time alive.
Most time that a full crew was together.
Most time spent playing music.
Most Hull repairs completed.
Most time spent on land (For all ye landlubbers-)
Most time spent at sea (For all ye scurvy knaves-)
Most times that someone fell overboard.
Explored the most
Most stolen treasurers
Most banked gold
Most ships sunk
Most added friends
Longest engagement at sea.
Longest kill shot.
Most distance covered by swimming;
Most mermaids ignored;
Most climbed up to the crows nest;
Most distance covered on your own ship;
Most distance covered on someone else's enemy ship.