I was wondering what the squeaking noises from my keyboard were. Now I know: hamsters. Damn rodents.
Argh. I was writing up a reply and Princhester beat me to it. Three times. 
Anyway, yeah, the Earth isn’t a point, so standing on the surface we won’t see half of a full orbit. For most things in low earth orbit (which are pretty much the only manmade things in space we can see with the naked eye), someone on the surface will only have a good view for at most 10-15 minutes, depending on the altitude of the orbit. That’s under perfect conditions, which are pretty hard to come by. So if it’s not visibly cruising across the sky, and it’s brighter than the stars, it’s most likely a planet.
The site that Shiva posted is a great resource for satellite related stuff. If you use Jpass to find an ISS pass that goes nearly overhead, you’ll see that the time between rise and set will be just over 10 minutes, assuming you live somewhere where it passes directly overhead (between 51deg N lat and 51deg south). Also, I suggest trying out jtrack 3-d, which gives a really great sense of the difference between low earth orbits (shuttle, ISS, lots and lots of useless crap, etc), medium earth orbit (mostly GPS and Glonass) and geosynchronous orbits (TV and communication satellites).