AM is inherently a worse modulation method. AM is Amplitude Modulation, which means that to encode an audio signal, you use the audio to vary the amplitude of the carrier signal, or in other words you vary how loud the carrier signal is. The disadvantage of this is that if you have two AM signals they add together, and there is no way to seperate them out from each other. Any noise on the same frequency also gets added in and you can’t get it out either. If the signal fades a bit due to atmosphere conditions, the audio signal also fades.
FM is better because instead of varying how loud the signal is, the audio signal is used to vary the frequency of the carrier wave back and forth. To decode the signal, all the receiver has to do is track the frequency back and forth. This means that weaker signals and noise are completely rejected. Additionally, because the signal just tracks the frequency, any fading of the signal only affects the amplitude and not the frequency, which makes FM immune to fading as well.
To make things worse, as chrisk mentioned, FM signals are set up by the FCC to have more bandwidth allocated to them. AM signals have a bandwidth of about 10 kHz (IIRC) while FM signals have a bandwidth of 15 kHz. Your ear can hear up to about 20 kHz, so while FM signals won’t sound as good as a CD, they will sound a lot better than AM to the average ear. Note that it is possible to make AM signals with a wider bandwidth. The FCC just chose not to, because back when the standard was put into place, you wouldn’t have noticed the difference on equipment at the time, and all that extra bandwidth means you can have less radio stations in the same amount of frequency space. Also, FM signals are set up to be stereo, while AM is only one channel (mono).
For all of these reasons (plus everything mentioned by previous posters), AM radio sucks for music when compared to FM. In the late 70’s and early 80’s, the quality of the typical radio in homes and cars got a lot better, and people really started to hear the difference. In the 70’s there were still quite a few radio stations on AM that were still playing music. By the 80’s, almost all of these had either switched to FM or had just gone away. Some car stereos started being made that didn’t even have an AM band on them. It was really starting to look like AM was a dead radio band, and there was a lot of talk about what should be done to either revive it or use the frequency space for something useful. There was a push for a while to have AM stereo, and to increase the bandwidth allocations for each channel. This doesn’t get you around the fade and noise problems, but otherwise it would allow AM to sound almost as good as FM.
In the late 80’s and early 90’s, talk radio started taking off. If you wanted a talk radio station, you had two choices. You could fight for space on the overcrowded FM band, or you could use some of the empty space on the dead AM band. Since voice signals don’t sound bad on AM’s narrow bandwidth, the lesser quality of AM wasn’t really an issue for talk radio. The next thing you know, the AM band is hopping with talk radio stations, and all of the talk about AM stereo and other methods of rejuvinating the AM band pretty much disappeared.