What do you like best?
Autodesk 360 allows you to store you work and share it in order to collaborate. It is easy to use in that it is (or at least with me) included in your download of Autodesk/AutoCAD programs. It is very easy to share you work with those you are working on, or store it in the "cloud" as to protect it.
What do you dislike?
Many programs come with access to a/the "cloud" now. The two clouds I use most are those belonging to Google and Adobe, and with Google being essentially universal and easy to log in to (since usually linked to your email), Google's cloud storage is what I use most frequently. I only use Autodesk 360 if requested. And while not a particular concern of mine at the moment, we have all seen via media that the "cloud" can be hacked somewhat easily, so it might not be best when security is the utmost importance.
Recommendations to others considering the product
It all comes down to your preference of digital storing of files. There are other programs and services that also offer the same functions as Autodesk 360, such as "Google". Personally, I don't use it due to cloud access via other programs.
What business problems are you solving with the product? What benefits have you realized?
Well, it helps with the issue of digital storage. Files from any rendering program are huge, and can take up valuable hard drive space, and this "can" help relieve that. Also, it helps protect your files if you suffer a fatal hard drive error or something, with the copies being store in the digital cloud rather than lost in the death of your hard drive.