What do you like best?
One of the best things about Rackspace, and probably the one thing that they champion internally is their support. Getting someone on the phone is super easy. Each time I've called, I've gotten someone that is US based, has a personality, and is intelligent about what you need help with. Their product offering is geared towards advanced power users (sys admins, engineering types) and they provide support with people who are competent in that area.
Not only are they responsive via phone, but also via chat, and their ticket system. If you need support, Rackspace will provide it. Their pricing isn't the cheapest, but it's not the most expensive either. It's a great value, and if support is important to you, you needn't bother looking any further for a cloud infrastructure provider.
Their stability is great, even when the hypervisor scares in late 2014/early 2015 came about with bugs that allowed attackers to break out of their virtual machine, they were responsive and orchestrated a huge upgrade across all their infrastructure. They achieved it in such a way that allowed us to avoid down time, despite our host machines needing to be rebooted. When they applied a second patch that required reboot later that year, they were able to achieve it without us having to do anything because they automatically migrated our virtual machines to different hosts.
I can't say enough about how great Rackspace is. They treat their customers with respect, and it's evident in the amount of effort they put into supporting them. I would definitely recommend utilizing them if you're in the market for cloud based server infrastructure.
What do you dislike?
Personally, I dislike having to log in to the web interface to do anything related to reading or creating support tickets. This is a minor annoyance, but being in the Rackspace interface isn't part of my day to day routine, so when I get ticket notifications (they create tickets for all communications), I can't read it in my e-mail. This is definitely a minor issue and certainly not a show stopper.
Probably the biggest annoyance is that their automated backup service is rather limited. With the Rackspace offering, they allow you to schedule automatic backup image creation of servers and storage volumes attached to those servers. However, these backups are limited in size. At last check, it was something around 80GB. This is certainly large enough to clone your machine configuration and it must've been designed for that. If you need/want to backup your data, you'll have to roll your own backup solution (either using a 3rd party, or your own tools).
One more dislike, the Cloud Files offering is incredibly slow. I/O on Cloud Files, when we were evaluating it, was so slow that it made it unusable for us. They may have rectified this in recent history, so if this is a sticking point for you - I'd advise you to do some more research.
Recommendations to others considering the product
Be realistic about your requirements. When looking at cloud providers, it's easy to get big eyes and launch huge virtual machines with 60+GB of memory just because you can. These servers are expensive (relatively), and because of the nature of virtual machines, you don't need to start off with the biggest hardware you can. You can easily step up to the next level when the one you're at becomes a bottleneck.
What business problems are you solving with the product? What benefits have you realized?
We started using Rackspace's Cloud offering in 2010 to host our MySQL database servers, after suffering 2 catastrophic crashes, and service unavailability, with dataloss on another provider within 30 days.
Since switching our database servers have been rock solid on Rackspace, and we continue to use them for other services as well. Our backups have only needed to be pulled out a couple times, but not for anything infrastructure related - just restoration of data that was accidentally changed (user error)