Solar System Simulator
Greylark writes "The Solar System Simulator lets you see a number of different planets and moons from a number of different positions in the solar system, at any day and time in a 800 year period." This is very cool, and even though it's been around for a while, we don't seem to have run it before.
A model of a solar or planetary system is called an orrery.
A Java Orrery Applet
Another Java Orrery Applet
If you're looking for these, including this word in your search will find a lot more. Many types of orrery have been made of brass for hundreds of years.
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NASA's site seems either down, slow, or slashdotted. There's also the Solar System Live (http://www.fourmilab.ch/cgi-bin/uncgi/Solar/actio n?sys=-Sf). It appears to be/do the same thing (though I haven't seen the NASA site).
The Good Reverend
I'm different, just like everybody else.
If you get Home Planet, other useful things are NISTime (freeware time synch program from NIST) available here, and you can get two-line satellite tracking (TLE) info (also useful at the Earth and Moon Viewer site) from NORAD's satellite catalog here. It's all text files, and there are several that are designed for automated downloads for the real fanatics.
In general, everything is surprisingly simple, and it doesn't take much to, say, get the latest telemtry on Endeavor (STS-100) here, cut-and-paste it into a Home Planet satellite database (text file), and see exactly where the shuttle is.