The cloud?

I have my cd library saved on external HDs and on thumb drives for use with my Bryston BDP-1/BDA-1 combo. Is there a way I can also save my music files to the Cloud? I'm boxing up my CDs and getting them out of my family room and placing them in storage.
Google Play Music All Access, which will run you $10 per month, will allow you to upload up to 20,000 songs. Depending on the speed of your Internet access, this might take about half an eternity, but you'll then have your tunes to access on whatever device you like, whenever and wherever you like.

There are other solutions, of course, but this one works pretty well.

-- Howard
... Depending on the speed of your Internet access, this might take about half an eternity.
Good point by Howard.

For example, if your upload speed is say 5 megabits per second, and if that speed is not further limited by the web hosting server at the other end (a big "if"), uploading 1 terabyte of data will require roughly 3 weeks of 24/7 operation.

-- Al
Just get a 2TB drive for $100 and be done with it. This whole Cloud thing is such a marketing joke!
It seems that unless you need to access music remotely due to travel, a cheap hard drive is the way to go. They can be small and many also have Bluetooth if that is useful for you.
I have 3 2TB drives from Western Digital. The first is one I use to listen to music with, the second is safely tucked away in storage as a backup and the third is in a safety deposit box in a bank.

At roughly $300 you are done!
PLex media server runs on your computer and enables hi res
remote internet access ( not just for audio but HD video
and photos) via web browser or mobile apps.

No need for files to leave your home or be copied to the
cloud which will take forever for a large library initially
as pointed out.

PLEX server is free as is browser access and just requires
setting up an account on site. Mobile apps are $5.

Plex has its quircks still but overall works and sounds

I run plex on an amazon TV box at home which supports high
res audio formats and has toslink audio out to your dac of
choice. Your hdtv becomes your user interface.

I also listen remotely using computer browser from work and
from various mobile phones and tablets.

This past weekend I was listening to my home music library
remotely while out of town in DC on an overnite vacation
using good quality headphones with my wife's iphone.
You can do this with Microsoft OneDrive. Not sure how the client is presented on a MAC but on Windows 8 and Windows 2012 Server the OneDrive client service maps a drive on your local machine to the cloud repository. It is like having a regular local drive. Of course there will be some latency issues with this and it will not be 100% reliable as a physical local drive. This will depend on external factors such as the reliability of your home internet and the reliability of Microsoft Azure Cloud. The company I work for is moving tons of apps and servers to Azure and we have had good success with Azure.

You have given me an idea of trying this myself with my JRiver WIndows 2012 Server system and Benchmark DAC2.
This whole Cloud thing is such a marketing joke!
Are you kidding? I use iCloud to backup my iPhone. It works great restoring a corrupted phone and initializing a new phone when I upgrade.