Online tools for Space applications are becoming more numerous everyday and many are quite capable.

Space Tools

Heavens-Above provides times of satellite visibility over your backyard with star charts showing its track.

Solar System Dynamics site by NASA JPL provides information related to bodies in orbit around our Sun.

Two-Line Element Sets are available from the Center for Space Standards & Innovation through NORAD.

Satellite Toolkit (STK) from Analytical Graphics, Inc. (AGI) is an industry-standard orbital analysis application (a Geosynchronous Transfer Orbit was modeled in the image below using STK, provided here as an example of tool functionality, courtesy AGI).
 

NASA TV features live television coverage of significant events, such as mission launches.

ESA Orbits is a cool interactive site that displays real-time models of ESA's satellites.