How many starships/battleships has Captain Zapp Brannigan lost that were under his direct control, throughout the course of Futurama's seasons and films?
If we count a "loss" as every time a ship is seriously damaged or destroyed (meaning that a repaired ship can count more than once) then I count 8 losses:
It crashed into the ground in "Fun on a Bun" during the battle with the Neanderthals.
In addition, you could count the stone Martian ship from "A Farewell to Arms" seeing as how Zapp had it purposefully dismantled, but that was after he successfully piloted and landed it on Mars.
His personal ship, the Nimbus has been destroyed several times. Two examples that immediately come to mind are "A Taste of Freedom" where the Nimbus is chopped in half by a crab like ship, and again in the movie Into the Wild Green Yonder while traversing a giant miniature golf course.