Install OS X inside a VMware ESXi server (hypervisor) Say you have a apple hardware, that you installed a VMware ESXi server, is it legal and possible to install a Mac OS X on that hypervisor, and access it remotely, say with RDP or Logmein or whatever to use it as a remote desktop environment?
Apple loosened restrictions around OS X and virtualization with Lion. Previously on OS X Server could be virtualized and even then, only in narrow circumstances. With Lion you could virtualize the non-Server OS X version.

The Mavericks EULA maintains the Lion virtualization clause. Specifically it says:


  (iii) to install, use and run up to two (2) additional copies or
  instances of the Apple  Software within virtual operating system
  environments on each Mac Computer you own  or control that is already
  running the Apple Software, for purposes of: (a) software 
  development; (b) testing during software development; (c) using OS X
  Server; or (d)  personal, non-commercial use.


So you can:


Only virtualize on Apple hardware (which you say you're doing);
Only virtualize non-Server for development, testing or "personal, non-commercial use" otherwise you have to use the Server version of OS X (which is a $20 add-on to Mavericks from the App Store)


Fall within the bounds of the above-mentioned restrictions and yes, you can virtualize OS X in your ESXi environment.