You can either use limited Web client or run vSphere Client in VMware Fusion or similar.
I believe next gen vSphere client will run in Web browser and is most likely based on Adobe Flex, I base this assumption on the fact that EMC CLARiiON and Celerra management on next flare version is based on Adobe Flex. If or when this will happen I have no clue.
edit. I have to add that like DAVESTR told you could use RPD to access vSphere Client on Windows VM, this is actually how I use the client daily, even though I have Windows on my laptop.