Download links for VMware vSphere Clients:
All downloads are direct links to VMware.
If you do not trust it, you will find similar information at KB2089791.
Q: Is the vSphere Client backward compatible?
A: Yes and No. You have to install a client for each version (4.0, 4.1, 5.0, 5.1 and 5.5) you want to connect to. Within these versions, the client is backward compatible.
At the end, you will nevertheless see a single vSphere Client at your desktop. It's a shortcut to the Launcher which will start the correct version after you've entered vCenter connection information.
Q: I can see different versions for vSphere 5.5. Which should i install?
A: Always use the latest version. The latest vSphere Client 5.5 client is compatible to all vSphere 5.5 versions. The latest clients are linked (and updated in the future) in this post.