I've had an iPod shuffle for almost a year. No problems. Everyone I know with an iPod has had them for years without problems.
I have heard of people whose iPods break...after "only dropping them a couple of times." Well, um, if you drop your computer several feet a couple of times, it probably won't work very well either.
I've seen and played with some non-iPod players. They've all had more problems (user interface issues, battery issues, software glitches) than my iPod.
Granted, iPods aren't perfect. They seem to be a fine choice, though.