Without Mars there would be many fewer impacts of asteroids on Earth. I mentioned this in a comment but I think it's worth its own answer.
The reason is the following. Near-Earth asteroids -- asteroids whose orbits cross Earth's -- are the population of asteroids that can bash into Earth. They don't survive for too long, only a million years or so on average, because their orbits are not stable for the long term. So, where do they come from? Well, asteroids in the main asteroid belt (between 2.1 and 3.2 AU) are somehow pushed onto an unstable orbit, typically an orbital resonance with Jupiter or Saturn, like the 3:1 resonance with Jupiter (where the asteroid makes 3 orbits around the Sun for every 1 of Jupiter's). These locations are called the "Kirkwood gaps" and are systematically devoid of asteroids:
On its way in to become a near-Earth object, the asteroid typically has its orbit stretched out (i.e., its orbit becomes much more "eccentric"). This causes the body's orbit to cross the orbit of Mars, and eventually the asteroid is usually kicked inward by Mars (whose orbital distance is 1.5 AU).
If Mars disappeared, then would asteroids still be able to move inward from the main belt to cross Earth's orbit? Yes, but with a far lower efficiency. Because as an asteroid's orbit gets stretched out, its closest approach to the Sun becomes smaller (and therefore closer to Earth) but its farthest approach becomes farther (and therefore closer to Jupiter). If the asteroid's orbit crosses Jupiter's it will be kicked out of the Solar System quickly.
Without Mars as a conveyor belt toward Earth, many fewer asteroids would be able to cross Earht's orbit and therefore hit us. So, the impact rate on Earth would be much lower.
Of course, the story would change if Mars' orbit were instead populated by a swarm of asteroids...