From:http://www.badastronomy.com/bad/misc/planets.html

Let's look at gravity first. Right away you can see that even mighty Jupiter, king of the planets, only pulls about 0.01 (= 1%) as hard as the Moon does (just to show how I did this, Jupiter masses 27,000 times the Moon, but is 1640 times farther away. The square of 1640 is about 2.7 million, and 27,000/2.7 million=0.01). Venus is next, with only 0.6 % of the Moon's force. After that, the numbers drop a lot. The total pull of all the planets combined is 0.017, not even 2% of the Moon's pull!

That ain't much. But is it enough to destroy the Earth?

No, it isn't. Think of it this way: the Moon orbits the Earth in an ellipse, which means that sometimes in its orbit it is closer to the Earth than others. At perigee, or closest approach, it is about 363,000 kilometers away, and at apogee, or farthest point, it is about 405,000 kilometers away. If you use these numbers like we did above, you see that the Moon's own gravitational effect on the Earth fluctuates by about 25% every orbit! The Moon orbits the Earth in about a month, incidentally, so it goes from apogee to perigee every two weeks. So every 14 days we see a change in gravitational effects from the Moon more than 10 times greater than all the other planets combined! To put this in even more perspective, the force of the Moon on you is only about 0.000003 times the Earth's. For me, that means I weigh an extra 0.4 grams (0.0009 pounds) more when the Moon is under my feet versus when it's on the horizon (and therefore not contributing to the downward pull of the Earth). Not much! [Oops! (January 13, 2001): A reader pointed out to me that I blew it here. Grams measure mass, not weight. I would still mass the same amount, but my weight will increase when the Moon is under me. Converting from units of weight (pounds) to mass (grams) is only good when you are in one gravity. So really I should have reported my weight in pounds, not in grams.]

Now let's look at tides. Venus stretches us the most of the planets, simply because it is the closest on average. But look! Even Venus only stretches us 5 hundred thousandths as much as the Moon does! This is completely negligible, and the other planets have even less effect. The change in tidal force due to the Moon's elliptical orbit is hugely larger than the combined tides of all the planets. It's worth mentioning that the "alignment" in 2000 has all the planets on the far side of the Sun. This means that you can add 300 million kilometers to the above distances, and I think you can see that the numbers will drop even more. For example, Jupiter's gravity drops from 0.02 to 0.005, and Venus' tides drop by a factor of 500!

Note again that the Earth still exists. Feel better now? Of course you do. Bad Astronomy, it would seem, has a much stronger influence on our minds than our bodies.