Helping people with computers... one answer at a time.
There are a few different reasons why music will not play smoothly on one's computer, depending on your hardware and how you're playing music.
When I play a music CD or try to listen to a wave file off the Internet the music "breaks up" and does not play smoothly. ... Do you have any ideas?
Several ideas, actually, depending on the situation.
If "playing a music CD" quite literally means inserting a physical CD into your drive and listening to it directly, then I'll immediately suspect your sound card. Either it's broken or extremely cheap. Most reasonable sound cards take the audio directly from the CD drive and route it to the speakers without your processor getting involved. I'd swap it for another and see if that doesn't resolve the issue. (If this is sound support on your motherboard, then this gets a little tricky, as you can imagine. You can try installing an additional sound card.)
If you're attempting to play an MP3 file across a network, or "live" as it's being downloaded from the internet, don't. Try downloading the file locally first and then playing it directly from your hard drive. If this works, then it may simply be a case of your internet connection not being fast enough to keep up with the data stream required to play the audio you've selected. If you're listening to streaming audio stations on the internet then try choosing one with a lower bandwidth requirement.
If neither of those applies, then things get interesting.
Chances are it's an interrupt or device driver problem. It's even possible that it's not even the sound card's, though it still might be. What could be happening is that a device is hogging the processor long enough to cause your sound card not to be able to push data to the speakers fast enough. Normally that shouldn't happen for two different reasons: a) other devices shouldn't be hogging the processor for that long, and b) your sound card probably shouldn't care if it had a big enough buffer.
Certainly I'd make sure that your system and device drivers were as up-to-date as possible. What means visiting both Windows Update as well as your hardware manufacturer's website to look for updated drivers.
It's possible, believe it or not, that you might be able to at least affect this problem by rearranging the cards plugged into the slots in your computer. Naturally this isn't something to be done lightly, but what can happen is that the devices can be assigned new priorities and the sound card might come out on top.
All that being said, I had exactly this type of problem some time ago, and walked away in frustration. The bottom line is that my machine had come with an incredibly cheap sound card that was in conflict with an equally cheap hard disk controller and there was nothing I could do with it.