As Boing Boing says, "In general, these disappearances have a couple of important details in common — they're usually relatively small craft carrying a small number of passengers."
However, I would like to put in a word for British South American Airways, which lost three planes in the years immediately following World War II. Star Tiger and Star Aerial remain lost to this day, while the wreckage of Star Dust was found on Mount Tupungato, on the border of Chile and Argentina, in 1998.
The most striking entry on the Wikipedia list is Walter Powell, Conservtive MP for Malmesbury, who drifted away in a hot air balloon in 1881.
A page on the town's Athelstan Museum website tells the story:
In December 1881 Walter Powell flew his balloon, Saladin, with two friends to take some meteorological observations. They found themselves being blown out to sea and had to make a rapid descent near Chesil Beach. They landed heavily and his two passengers and some ballast were thrown out; one of them breaking his leg. Powell stayed in the basket but the balloon, now much lighter, took off once more. Water Powell was last seen waving to his companions as the balloon disappeared out to sea.
He was never seen again.A by-election was held in Malmesbury the following year.
Is this the only by-election ever called without the previous member's resignation or his body being found?