There are lots high-quality software packages written for amateur astronomers, a great many of which are freeware. Following is a list of my favorite programs, with links to the sites where you can download the software for your own use. This is by no means an exhaustive list, and includes only the programs that I use regularly for my own backyard observing program.
Cartes du Ciel (Sky Charts)
An excellent program which generates charts or planetarium-style views for any given time and location. You can print the charts for use at the telescope as well.
Virtual Lunar Atlas
A great program for identifying lunar features, or for planning an upcoming lunar observing session. Be sure to download the add-on orbiter photos as well.
Home Planet
Another planetarium-style program. While not as powerful as Cartes du Ciel, it has some unique features of its own, and is extremely easy to use.
Mars Previewer II
A program that shows the appearance of Mars at any given time and location. It identifies surface features and gives you an idea of what you might see in your telescope on a given night.
Satellites of Saturn, Galilean Satellites, and Jovian Moon Events
DOS-based programs for identifying the moons of Jupiter and Saturn, and for predicting Jovian moon
events such as eclipses, shadow transits, etc. This last program produces an output file that is similar to the monthly tables in Sky & Telescope magazine. (Be warned that it runs very slowly on all but the newest computers.) I used all three of these programs a great deal until I found Meridian, below.
Meridian
A fantastic program for planetary observers. Meridian computes everything you'd ever want to know about the moon & major planets, such as rise & set times, visual magnitude, apparent diameter in arc-seconds, opposition and conjunction dates, etc. It includes the position & identification of the moons of Saturn & Jupiter, and has a utility for generating a text file of Jovian moon events (which I like to export to my handheld for easy reference). There's not much in the way of a help file, but it's pretty self-explanatory, and highly recommended. One helpful hint: Users should note that unlike most astronomy programs, Meridian generates most of its outputs in your own local time, not Universal Time. Also, the program does not automatically switch to Daylight Savings Time. (As long as you're aware of this, having the output in local time actually makes it more convenient.)
Celestia
A graphically stunning 3-D model of the universe, which lets you virtually "fly" to any point in space. While not particularly useful from an observing standpoint, it's great fun to play with if you have a decent graphics card.
Software for PalmOS® Handhelds
Not all great astonomy software requires a PC! Click here to jump to a second page which lists my favorite software for PalmOS handhelds.