Here is my roundup of the current options:
1. External Hard Drive - This one is pretty straightforward. Buy a cheap backup harddrive (amazon affiliate link) and copy your music files. If you are a mac user, I recommend setting-up time machine, which will automatically back up your music files as well as the entire contents of your computer hard drive.
For windows users, there are a number of backup software options available, including the built-in windows backup program. You can also just copy and paste your music folder directly into your external hard drive.
One recommendation - you may not want to leave your external hard drive plugged in at all times. If you have a massive power surge at your home, you could end up with a fried computer and a damaged external hard drive - and lose your entire collection.
2. Google Music - Music by Google is still in its beta, but for now you can back up your entire music collection at no upfront cost. If you get an invite, you can use the Google music manager to upload your entire music library.
The downside is that, depending on the size of your music collection, the process can take days or even weeks. My library took me 7 days to upload. Once uploaded, google offers a very nice web interface to stream your library. They also have a pretty good mobile app to stream your library on the go. Android users have the advantage of a Google music app to access their collection.
The other questionable feature is the inability to download music that you have uploaded to your library. The only current option to access your music is through streaming via google.
3. Amazon Cloud Player - Amazon offers a similar program as Google for backing up your music in the cloud. You can use Amazon's mp3 uploader to upload your entire collection. Again, this process can take a week or more to complete, depending on the size of your library.
Amazon does give you the ability to download your music files onto your hard drive and then load onto an mp3 player. They also have a nice web interface for streaming songs and an Android app. However, they currently do not offer a mobile web app for iphone users.
Amazon is currently offerring unlimited space for music for $20 a year plus an additional 20GB of general cloud storage included. However, they advertise these costs as a limited offer.
Another cool feature is that music purchased via the Amazon mp3 store is automatically and instantly available in the cloud.
4. Itunes Match - Itunes match is Apple's answer to cloud music storage. Its a different take on music backup in that it scans your music collection and provides a matching itunes AAC 256kbps file for every song that is available in the itunes library. This drastically cuts down the time it takes to "upload" your music collection. If a song in your library does not contain a matching itunes file, then Apple will upload your own digital copy into the cloud. For me, this was about 200 songs to upload instead of 8,000 songs through Google and Amazon. Plus, any song that you purchased via itunes is already available for you in the cloud as a backup.
Itunes match can sync with your IOS devices so that you have instant access to your entire library at all times from your iphone, ipod touch, ipad, and itunes software. Music can be either streamed or instantly downloaded to your ios device for playback.
The service costs $25 a year and is scheduled to launch in the near future.
Whatever service you choose, I would recommend a combination of an external hard drive and cloud storage. I have tried all of these services so I currently have 3 cloud backups plus an external hard drive backup of my music collection. At this point, it would take a pretty massive disaster for me to lose access to my collection.