We probably wouldn't be dead, because we'd never have lived. Without the tremendous gravity of Jupiter to vacuum up asteroids and comets straying in toward the gravity of the Sun, Earth would be the most massive object close to the Sun and would take the bulk of the impacts. The comet that hit Chicxulub 65 million years ago, ending the age of the dinosaurs, was about 6 miles in diameter. Halley's comet is 20 miles in diameter. Earth would not likely have ever even developed complex life had Jupiter not been out there to take the devastating hits for us.

Jupiter, which has a mass three times the combined mass of all the other planets, dominates gravitational interactions within the Solar System. But even if it suddenly disappeared there would be very little impact on the movements of the other planets, which are mostly determined by the Sun’s gravity.

Cosmologists now think that during Earth's early days, Jupiter's orbit migrated closer to the Sun and its massive gravity disturbed objects in the asteroid belt and Kuiper belt causing some to hurtle into Earth in the Late Heavy Bombardment between 4 billion and 3.8 billion years ago.

It appears that bombardment brought with it ices that here melted into our oceans, and also numerous organic chemicals forged in the high-energy radiation of space from the elements of life into proteins and amino acids that formed the perfect primordial soup from which life could spring. 

 

An earlier pass within Jupiter's Roche limit by the comet in July of 1992 shredded Comet Shoemaker–Levy 9 into 21 separate pieces stretching more then 3 times the distance from the Earth to the Moon and ranging up to 2 miles in diameter.

On the comet's next swing into the inner Solar System, these pieces made final impact with Jupiter's southern hemisphere between July 16 and July 22, 1994. The impact marks seen in the previous photo of the planet remained visible for months.