Yes Copy and paste is supported, but it depends on what you are doing. If you are trying to copy and paste files using a right click and copy command in the Finder, and then trying to right click and paste in a Windows VM for example that will not work since VMware does not support copying files that way. When moving files between VMs Drag and drop is the feature to use (where supported with VMWare tools, etc)in order to move files from the host computer to each guest VM and the opposite is true too.
Now if you want to copy text using the clipboard, that works between the host and each supported virtual machine with the tools installed as noted in Moving and Copying Files and Text Between Virtual Machines and Your Mac
You can drag files and folders to move and copy them between your virtual machines and your Mac. You can move text by copying and pasting or cutting and pasting.
You can also drag images between Windows applications and Mac applications. You can drag Outlook attachments from a Windows virtual machine to your Mac. You can drag files in a virtual machine directly onto Mac applications.
You can copy and paste images and formatted text between a Windows or Linux virtual machine and your Mac.
For example select text in a Mac OS X application and copy it to clipboard (Command-C). Then go into a windows VM and put your cursor in a text area and then perform a control-v you should get what you originally copied on your Mac host.
According to other documentation for VMware Workstation
The copy and paste feature has the following restrictions:
• Copying and pasting email attachments is restricted to images or files smaller than 4MB.
•Copying and pasting plain text and formatted text (including the formatting) is restricted to amounts less than 4MB.
•Copying and pasting text is restricted to text in languages that can be represented by Unicode characters.
•Workstation uses the PNG format to encode images that are copied and pasted. Copying and pasting images is restricted to images smaller than 4MB after conversion to PNG format.
•You cannot copy and paste files between virtual machines.
•On Windows 95 and Windows 98 guests, copying and pasting is restricted to plain text in amounts less than 64KB.
The Vmware Fusion for Mac Documentation fails to mention any limitations on copy paste size limits, etc but it is same to assume the limitations are probably transferable to the Mac version of VMware as well.