To get extremely simplistic about it: For: need fewer physical machines, taking up less space, less network connections on the switch, and less power. Against: requires a bigger more powerful machine than one dedicated to any single task. Also learning curve, how to set it up properly.
Against is actually a For since the bigger more powerful machine uses less power than multiple smaller ones. It also makes backup easier and also replacement. However it's putting all your eggs in one basket.
If you are a business, just skip the answer, because you should be virtualised already. If you are a nerd, play around and have fun If you are a developer it's nice to have different test- and build environments If you are interested, it's a lot fun to learn about the future. If you are playing serious games, just skip it. If you like to experiment with a lot of (illegal) downloaded, maybe infected, software it's smart to use. If you are not in one above you should not be on this forum And I think I missed a lot: If you ares....
Virtualization gives you the power to improve app performance with fast provisioning and dynamic load balancing, and fast disaster recovery. You can utilize your hardware by consolidating your servers on less machines. The average server uses about 10% of what it is capable of. If you use virtual servers, you can use one machine for many servers. Will save you big money in the end on hardware and electricity.
Actually, what is required is a larger HDD - not necessarily a larger anything else. I started playing with virtualization with vmWare, VirtualPC, and VirtualBox (before and since Oracle acquired it) and I'm playing with Hyper-V today (desktop and the newer of my two notebooks). Given that the original platform was a Celeron E3400 (I don't remotely kid) with all of 2GB of DDR2, it's still "what do you want to virtualize". vmWare, the old VirtualPC, and VirtualBox all require nothing more than VT-x (the same is true of Hyper-V in Windows Server or Hyper-V Server 2012R2 and earlier); Windows 8 and later (Pro and Enterprise only) and Windows Server/Hyper-V Server 2016 all require EPT/SLAT support (PentiumG3220 and newer, including G3258, and AMD Turion II and later). The one advantage vmWare and OVB have over Hyper-V is support for MacOS X guests. For common guests with identical host settings, however, it's Hyper-V in a walkover, and nowhere is it more obvious than with (of all OSes) Android.