The pointers for most of the programs are to ftp sites (although I keep a few of the smaller files locally). At busy times of day, you may have a difficult time connecting. If you have trouble connecting, just try again at a different time (all sites are in the U.S., so you can figure out which times might be busy and which not).
EarTest is an ear training program. It is loosely based on the method described in the David L. Burge Perfect Pitch ear training course that you may have seen advertised in music magazines. EarTest plays a note, you must respond by playing the same note on a MIDI keyboard. It has several levels, from very easy to incredibly difficult. If you don't believe in learning perfect pitch, you can use it to hone your relative pitch (you begin by learning the notes of the C major scale, so you can just think of do-re-mi and forget the perfect pitch stuff if you like). Requires MIDI card & keyboard. (DOS freeware)
Winoye, a cool ear training program for windows. Plays melodic intervals, harmonic intervals, short melodies, and two- and three-note chords, which you must play back by pointing to keys on a keyboard it displays. Requires a MIDI interface or a sound card. (Windows shareware.)
The Piano Professor has a variety of activities to help in learning music (note learning, ear training, chords, key signatures). It is big (1.5 meg zipped) and kind of slow, but it looks nice and is pretty easy to use. Requires MIDI interface or sound card. (Windows shareware.)
PC Piano Tutor also has a variety of activities (note learning, ear training, rhythmic dictation, reading intervals, steps and skips). It doesn't require MIDI--sounds are played through the PC's built in speaker and the student must respond through the normal PC keyboard (MIDI support is promised in the registered version). (DOS shareware.)
MusicCalc 2 calculates and displays chords and scales in all keys, major and minor. It displays the roman numeral chords (I, II, III, etc.) as well as secondary dominants, borrowed chords, seventh, ninth, and eleventh chords, and so on. It also has a self-test mode, so you can see if you know all these chords in all these keys. It displays the chords in functional notation (i.e., ii, V7), staff notation, and on a piano keyboard or guitar frets. It seems to be designed as a review or self-study help for a first year college theory class. (DOS freeware.)
Musicware Piano (demo version) is a full blown piano teaching program. I believe it is intended to be used alone, without a teacher at all (it certainly could be used that way), but it would be a nice complement to regular piano lessons as well. It looks well-designed, with lessons grouped into units and each lesson and each unit seeming to have a well-defined teaching objective. It can handle multiple students easily. This is a demo version, which means you can try a few things and see how it works, but it basically doesn't work unless you register. It is large (over one megabyte, compressed). Requires soundcard with synth drivers or a MIDI keyboard and interface. (Windows demo.)
Here is another site you can try for Musicware Piano (demo version).
Musicator (demo version) is a music notation-midi sequencer program. (Large--over one megabyte compressed.) (Windows demo.)
Information about the Computer Science Telecommunications Program at the University of Missouri-Kansas City