From this page you will find links to predictions for a number of visually observable satellites including the International Space Station (ISS) and during a mission, predictions for the US Space Shuttle.
For details as to what phenomena you might see, follow these links to the shuttle and the ISS.
Heavens-Above at Munich, Germany provides graphical predictions for the brighter satellites and also Irdium Flare predictions. The site provides tools to obtain your geographical coordinates. If you're new to satellite observing, you might want to look at the beginner's guide for basic terminolgy.
Arnold Barmettler's CalSKY provides predictions for satellites and most other celestial objects.
Michael F. Henry operates a visible satellite notification service called See-A-Sat, which charges a fee ($1.99 per month) to notify subscribers via email when selected satellites are visible at their location on the earth.
Predictions for the Shuttle and International Space Station (ISS) for various locations are furnished by NASA's Space Flight.
If your web-browser has Java capabilities, find predicted sky-tracks for satellites including the Shuttle (when it's up), the ISS at Marshall Flight Center's Lift-Off J-Track 2.5. There you can find 3D views of over 500 satellites in real-time and you can subscribe to e-mail list for obtaining up to 10 satellite predictions for your area.
Then again, you could cook up your own predictions. You'll find details on some software packages, pointers to element sets and other resources.
Links: to the VSO Home Page, and the Tracking Programs and TLE Resources page.