Hardware requirements vary wildly depending on the configuration. It is impossible to provide definite requirements, so any production installation should evaluate them individually. For our test environment, though, even as little RAM as 128 MB should be enough. CPU power in general won't play a huge role; Pentium II-class hardware should be perfectly capable of dealing with it, although generating graphs with many elements or other complex views could require more powerful hardware to operate at an acceptable speed. You can take these as a starting point as well when installing on a virtual machine.

Of course, the more resources you give to Zabbix, the snappier and happier it will be.