Instrumental music
It should be noted that Instrumental music is a very broad classification. Doing a search will bring up (amonst others) Karaoke, backing tracks and a host of other sub categories.

I was mostly concerned about the needs of some people arriving at my site in search of something other than backing tracks.

To my surprise, once I had set up the shopping cart below with all the products available, I discovered that by typing in a band or Artists name, There were a whole host of unexpectedly delightful results.

Give it a try - you could even end up with Led Zeppelin Karaoke and guitar backings, or some other surprises.
Enjoy.
My Amazon Instrumental Music Store

Make your own instrumental music
If you're keen on making your own background music, or want to learn how to make your own instrumental backing for an original composition, or some lyrics you've written

You could give Sonic Producer a try. While it's designed more for how to make your own songs as opposed to copying other peoples stuff, it will get you started on your own music production.

I personally use a lot of older software, mostly because I'm used to it and I've developed a lot of neat little tricks to get things done,

But when I first started out, I earned nothing for a whole month because I didn't know what I was doing.
Sonic producer is a lot easier to work with, and teaches you everything you need to make backing tracks.