What effects do other planets have on the solar system? For instance, Jupiter is the biggest planet in our solar system. Due to it's gravitational mass it can deflect meteorites and protect Earth from the Oort cloud.  While these are positives, the negative effects are that Jupiter can draw comets in from the Kuiper belt which may have catastrophic consequences.  

Do other planets have a similar effect on the solar system?
The gravitational pull of all the planets and the sun, and the rest of the galaxy and the universe, all play a part, but gravitational effects fall off with distance.

For Earth's orbit, the Sun is far and away the single biggest influence. Jupiter perturbs our orbit slightly, but with it or without it we have a simple elliptical orbit round the sun. We can measure the perturbation in our orbit from all the planets, but the effects are minor.

When it comes to gravitational effects on small bodies passing one of the planets, however, the effects can be dramatic - an asteroid passing close to Jupiter will be moved far from its original path. The same would be true when passing close to Saturn or in fact any planet - just to a lesser degree.

So while you can't say that Jupiter protects Earth from anything, especially not the Oort Cloud, you also can't say that it draws objects in. Anything out in the Kuiper belt or Oort cloud will be orbiting the barycentre of the solar system (which is within the Sun) and will keep doing that unless knocked out by something  like a collision with another object, or the pull of other Kuiper belt objects like Pluto, which can give a much greater tug.