Did you know you can regularly see the new International Space Station with the unaided eye? ISS looks like a medium-bright star (typically between 1st and 4th magnitude) moving across the sky, generally from west to east. It can also be fun to try to follow with binoculars or a telescope. The first two components were launched in late 1998; it will get brighter as more modules are added over the next five years. Here are a couple of web sites which generate visibility predictions for your location. Both sites give the time, azimuth and elevation for each overhead pass, as well as when during that pass the station is hidden by earth's shadow.
You pick your viewing location from a list major cities. Azimuth is given to the nearest degree. This site also gives the viewing info for the Space Shuttle, the Russian space station Mir (due to be de-orbited later this year), the Hubble Space Telescope, and several other selected satellites.
This site by the German Space Operations Centre gives the azimuth by compass heading only (for example, NW), but it also gives you the visual magnitude and range in kilometers! It also gives predictions for Mir, Iridium flares, and lists all satellites visible from your location on a given night. You can pick from a list of major cities or enter your exact location in latitude and longitude (this is especially important for Iridium flares, which are very location-sensitive).
One hint: the orbit does change over time, so be sure to download a fresh prediction within a day or two of when you plan to observe. Good luck and good viewing!