What Makes Google Play Music Awesome!

Google Play Music (free tier)

Pros:

Upload up to 20,000 songs of your current collection (at up to 320kbps).
Unlimited streaming of your music (and any purchased music) to any of your devices. Including and desktop with access to a browser, Android, iOS, etc.
Easily cache and download music offline on your phone so you can still listen in low/no-reception areas.
No need to setup your music when moving to a new device / computer. Just log into Google Play Music on your browser and you are ready to play your library.
Centralised playlists, play-counts and other data.
Very nice "Instant Playlists" that allow you to pick a base song or artist to play music from.

Cons:

Not able to access the online portion of your library if your internet drops out.
Initial upload can take a while depending on the size of your library and your bandwidth.
Constantly streaming music, you probably want a good data plan (or prepare your device for offline use ahead of time).

Above is a very quick breakdown of the pro's and con's of the free tier of Google Play Music. As you can see by just the number of Pros vs. Cons, it is a pretty damn good option for music listening.
The rest of this article goes into my experience and all the little things you get used to and the awesome benefits of Google Play Music in a fair bit of detail.
I would also like to note that all the con's are almost all based around internet caps, bandwidth and availability. If none of these are a problem for you, then I would highly recommend Google Play Music. However if you do have internet caps at home, it may mean you need to stage the upload (or upload during off-peak periods, or even at work). If you have an internet cap on your phone, plan what are your favourite songs you want to listen to while you may be out and about, and click the 'pin' icon on an artist or album to download that group of music to your device. The Android app has a toggle at the top of the screen where you can select between on-device and all music, this allows you to only listen to on-device music if your reception isn't that great or you are worried about your internet cap.
The initial upload of my 40gb music collection took about a week. The first time I tried to upload my library, the uploader client for Linux kept on crashing. This deterred me temporarily but when I saw another announcement about changes to Google Play music several weeks later and decided to see if the bug in the client was fixed. Sure enough it worked seamlessly and uploaded the rest of my music collection. The leads me to the assumption that the Windows, Mac and Linux clients must all be working quite well right now.
One of the really nice benefits I found was the centralisation of my music data and metadata. Having 3 computers (desktop, laptop and work) and 2 mobile devices (phone and tablet), the play-counts, metadata, playlists and which songs were actually on which device got out of hand pretty quickly. Having all my music and the data / metadata of it all in the one place means I can clean something up without worrying that I will have to fix it up on another device again later.
Instant Playlists in Google Play Music are just amazing. So many times I want to just listen to songs that are like some other song. I don't want to spend five minutes looking for them, I want it to happen automatically, and this is exactly what Instant Playlists do. You simply need to select a song, artist or album and click "Start Instant Playlist" and boom your are listening to a custom playlist selected from similar music in your library. Pretty mad huh?

Google Play Music: All Access (~$10US a month)

Pros:

Unlimited listing to, switching between, scubbing back and forth of all the music in the Google Play Music Store (unlike Pandora where you have limited skips and can't scrub).
For all you pirates out there, a cleaner conscience. Due to the fact that about 80% of the music you pirated you now legitimately have access to.
For all you legit-purchasing music lovers out there, $10 a month is less than one album. So if you regularly buy music, then this is a no-brainer.
Instant Playlists become "Radio Stations", that no longer just select music from your library, but similar music from all of the Google Play Music Store.

Cons:

If you stop paying, you stop getting the music. So if you think you might love music, but not $10 a month worth, then it is probably not worth opting-in to All Access.
You can't download any of the All Access music offline (for obvious reasons).

I do have to say, that for the past few days since I have been in the All Access music 30 day trial, it has been pretty cool being able to just browse the store listening to full-length tracks and add them to my library. I can drill down through Genre's (and Sub-genres!) and look at top albums and new releases from them.
That said, if you don't think you could get comfy paying $10 a month for music, then it may not be worth it. You are also getting a good service too, I certainly don't spend $10 a month on music, but I could see myself using this service enough for me to validate the cost.
If you haven't even tried Google Play Music yet, go in and upload all your music. Try it for a bit and get used to it. If you feel confident it is how you like to listen to your music, then try out the All Access 30 day trial. The 30 days should be enough to give you a feel for how much you think All Access is worth to you.
Link to Google Play Music
Happy Listening!