Other planets have almost no effect on Earth's gravitational pull. All objects (including planets) are attracted to each other by the force of gravity. How strong this attraction is depends on the size of the objects (mass) and how far apart they are. Earth?s gravitational pull on an object depends only on how far away that object is and the mass of that object. The total gravitational pull that the object feels could be affected by other large objects nearby, but because the other planets are very far away, the strength of that gravitational attraction is extremely small and can be ignored.

Even though the sun is also very far away its gravitational pull on the planets (including Earth) is much stronger than the pull of the planets on each other because it so much larger than any of the planets. (The sun is over 1000 times more massive than Jupiter and over a million times more massive than Mars). So all of the planets (Earth included) travel around the sun in elliptical (that is, nearly circular) orbits. A planet?s orbit can be very slightly changed by the gravitational pull of another large relatively nearby planet. This small effect will be greater the farther the planets are from the sun, the closer they are to each other and the larger they are. Although this effect is very tiny, it can be measurable. In fact, before Neptune was discovered, 19th century astronomers noticed irregularities in Uranus’s orbit and realized that this was a result of the gravitational pull of a planet beyond Uranus (i.e. Neptune). They were even able to correctly calculate where this “new” planet should be.

Good question! It sounds like you have already figured the important point, that other planets affect the Earth’s gravitational pull. In fact anything with mass in our solar system (and beyond our solar system for that matter) will have an affect on the Earth’s gravitational “field”, but the affect is really small for bodies that are far away. The reason for this becomes clear by looking at Newton’s Law of gravitation:

F is the gravitational “force” between two objects, m₁ and m₂ are the masses of the objects, G is the gravitational constant (a number that always stays the same), and r is the distance between the objects. The r term is “quadratic” (r² = r times r) and it is in the denominator (the bottom of the fraction). This means that when the distance between two objects (r) gets bigger, the gravitational force between them gets really small. This is why we are not pulled off of Earth by other planets in our solar system. Big objects, like Earth, definitely feel the affect of other solar system bodies though. This is why the planets orbit around the sun, which contains over 99% of the mass of our solar system.

Maybe I am getting off course of your original question. In short, the way that other planets affect Earth’s gravitational field is very complicated. The gravitational field that we “feel” on the surface of the Earth is basically the Earth’s gravity and the gravity of all other massive objects in our solar system (and beyond) added up. We “stick” to the surface of the Earth because the gravitational force between us and Earth is really strong because we are so close.

The force of gravity between two objects depends on the mass of the two objects and the square of the distance between them.

F = Gm₁m₂/r²
G is the gravitational constant (6.674×10⁻¹¹ N m² kg−2¬)\
m₁ is the mass of the first object
m₂ is the mass of the second object
r is the distance between the centers of mass of the objects

If the objects are very massive, then the gravitational force between them will be very strong, but if they are far apart, it will be weak. Since the distance, r, in the equation is squared, it has a stronger effect on the force than the mass of an object.

The gravitational force between the Earth and a 50 kg (110 lbs) person standing on the Surface of the Earth is ~500 N (a Newton, N, is a unit of force). The Sun is 333,000 times more massive than the Earth (more mass increases gravitational force), but it is also 150 million kilometers away (distance decreases gravitational force). Since distance is more important in determining gravitational force, the force between the Sun and a person on the surface of the Earth is much smaller than gravitational force the Earth exerts on that person. It is so small (only 0.06% of the force from the Earth) that you would never notice it in every day life. The force a person feels from the Moon is even smaller, 0.00035% of the gravitational force from the Earth, and the force from Jupiter when it is closest to the Earth is even smaller yet, only 0.0000037% of the force from the Earth.

The gravitational force between the Sun and the Earth is about 3.54x10²² N. This force keeps the Earth orbiting around the Sun. The gravitational force from the other planets does slightly affect the Earth’s orbit, but the gravitational pull from the other planets and the Moon is still very small. The gravitational pull of the Moon on the Earth is only 0.55% of the gravitational force between the Sun and the Earth. When they are closest to the Earth, Jupiter only exerts 0.0062% of this force and Mars only 0.00023%.

References:
http://solarsystem.nasa.gov/planets/index.cfm
http://nssdc.gsfc.nasa.gov/planetary/factsheet/
http://en.wikipedia.org/wiki/Newton% 27s_law_of_universal_gravitation