Their REST API is easy to use and implement. In the years they've dropped charging for several type of API calls which has made the service a bit cheaper. Storage prices are cheap.
Back when I was still using it was not possible to delete a container that had files/objects in them. There was also no way to organize your files in directories. Instead, you had to name your files something like "my directory/file.txt" and use that to resolve directory structure. This also made it harder to list only a small set of files inside a directory. Maybe this has changed now.
While storage pricing was cheap I did not like the costs for data transferring.
I've worked with Rackspace Cloud Files (and before that Mosso Cloud Files) for a while and mainly used them as a backup service. I've written a module in BlitzMax which uses their REST API and with that module I wrote a little GUI app that lets you synchronize a folder on your desktop with your Cloud Files account. I've also maintained the Perl module to interface with Rackspace Cloud Files.