Free, That's the most important thing about VMware player. It's available on both Windows and Linux. VMware used to only run a virtual machine / virtual appliance, but now we can create a new VM with VMware player. You can even redistribute VMware player with permission from VMware, it might be useful if you want to send demo of your product as virtual appliance to your client. We don't need dedicated machine to install VMware player, we can just use our desktop to run VMware player.
Room for Improvement:
Not available on Mac OS, so the only virtualization solution from VMware for your Mac OS is VMware Fusion. Lack of some features that only available in VMware workstation or VMware Fusion such as Teams, multiple Snapshots, multiple Clones, and Virtual Rights Management. Compared to Virtualbox, VMware player is slightly heavier on resource usage than Virtualbox.
Simple free virtualization solution that you can depend on. A lot of virtual appliance on VMware virtual appliance marketplace.