What do you like best?
I love the fact that Parallels lets me use all the goodness that is my Mac, while developing for various platforms - without having to mess around with having a dozen physicals or VM's on remote sites (e.g. Azure, Amazon).
Once of the nicest features of Parallels is the Coherence mode - which lets me have - say a Visual Studio IDE, or another IDE instance running withing my Mac - with full copy/paste ability. I can use tools that I need to running on Windows or Linux - without having the pain of rebooting or feeling like I'm going from one user experience to another - everything is seamless - and that's the beauty of Parallels - it lets me forget about it and focus on what is important - my work.
Another key feature is that Parallels supports vagrant out of the box and without having to pay an extra fee (as is the case with VMWare Fusion or Workstation if you want to use it with Vagrant - you need the VMWare plugin - which costs). The Parallels Vagrant plugin started life as an open source project, and remains that way - though under the direct custodianship of Parallels themselves.
Vagrant allows me to tear up VMs on demand for when I'm working on applications that require me to do that, it also allows me to prep-up my Docker containers ready for deployment remotely.
There is a lot more I could write about Parallels - and I've been an avid user since I moved from Windows to Mac over 5 years ago now - it let my transition be smooth and pain-free, and it has been a regular feature in my Applications folder, politely letting me forget about it, while allowing me to utilize all of its amazing goodness - letting me get the most from my Mac.
What do you dislike?
Whats do dislike - nothing as far as I can see, apart from perhaps as one of my colleagues had said - why isn't there a Windows or Linux version of Parallels - why is it only a Mac product? I couldn't answer that - but since I used a Mac - arguably I didn't care. However - that would be a major plus, if Parallels Desktop could be ported to Windows and Linux - that way, the Linux users wouldn't have to use Virtualbox and the Windows users Hyper-V or VMWare.
Recommendations to others considering the product
If you're not sure about Parallels - then take advantage of the free trials on offer, I'm sure that once you've started using it - you will not begrudge paying the subscription and becoming a true licensed user.
The beauty of Parallels is that once its installed and configured, you can totally forget about it. In my opinion, when a piece of software can be forgotten about while providing the services it providers - that's when it has moved to perfection.
Don't take my word for it, don't believe the marketing hype, TRY it - take advantage of the free trial.
What business problems are you solving with the product? What benefits have you realized?
A key business problem would be when users don't want to use Windows machines - for many reasons. This allows the work to proceed, within Windows - while the user can continue to use their Macs.
For a development house - this helps massively as it allows developers to continue building Mac and iOS apps on their macs - while having the ability to do the same - via Parallels - for Windows Phone (Windows), Android (Linux)*
*I'm aware that Android apps can be developed directly on a Mac, but some people choose to not do things that way - Parallels allows us to have that flexibility.
Another issue that was resolved was the ability to use Parallels with Vagrant to prep provisioning scripts ensure they are perfect, before pushing them out to Amazon, Azure or another cloud provider.