What do you like best?
Functionality is built-in to Windows Server 2012 and 2016, as well as Windows 10 Pro - so need to purchase a separate VM solution. It integrates with Windows Server Backup very nicely, making it very easy to backup a VM. Since Hyper-V functions as a server software, can manage multiple VM's hosted on multiple physical machines from a central location.
What do you dislike?
Initial setup can be clunky, and Microsoft's documentation, while vast, can be quite dense. Attaching physical hard disk to a VM, either internally or externally, is a lot more complicated compared to other VM solutions (specifically VMware's offerings). Compressing a virtual disk image (vhdx) can be a lesson in frustration as the compression doesn't always succeed. Support for non-Windows OS' is very weak - it will work with Linux, but drivers are weak. GPU performance for VM's is pretty awful, which leads into Hyper-V is primarily focused on hosting server OS' and is not designed for consumers in mind.
Recommendations to others considering the product
For the most part, Hyper-V meets virtualization needs. It is not as feature rich or as powerful as VMware vsphere or similar solutions, but being built directly into Windows is a major, major plus.
What business problems are you solving with the product? What benefits have you realized?
Hyper-V is being used to virtualize a number of different servers, including a Windows Server 2012 Domain Controller, a Linux Debian machine hosting an open source library management server called Koha, and a Windows 10 machine used for remote Quickbooks access. Benefits are multi-fold - being able to run multiple virtual machines on one physical machine cuts cost significantly. The ability to backup the entirety of a VM - system, applications and all - makes restoring in catastrophic scenarios much less painful. Having a central place to manage the various VM - even if spread across multiple physical machines, make monitoring and maintaining them much easier.