similar to multiple x sessions

While you have access to X on Mac OS X, what you're asking for (multi-seat X Windows or Terminal Services on Windows) is not available with native software and the direct analog is the AquaConnect third-party product. The Mac GUI doesn't have native multi-user.

Remcycle wrote:
I know that on linux you can initiate multiple x sessions so that when you connect to the computer using VNC and use the mouse and keyboard without interfering with what the user on the computer does.

X and VNC are two different things.

Is there some way to start a new session on the mac and do that same thing?

Sure, but you would be restricted to the same ugly X11 programs as on Linux.

There is a "Poor Mans" approach, but it has limitations.

Install the Vine Server (aka OSXvnc)

Enable Fast User Switching.

Use Fast User switching to switch to the 2nd account

Launch the Vine Server on this 2nd account, and configure it for a unique VNC port (eg. 5901)

Fast User Switch back to the 1st account.

Now from a remote system VNC to the Vine Server session on the configured port.

The obvious limitation is you have to set this up in advance.

It has been reported that some events that occur on the 1st account may affect performance on the 2nd account.

TL;DR version - not really.

Long winded version...

Much of the apple magic in making X11 work within the Cocoa on top of Aqua on top of Quartz/OpenGL/QuickTime stack makes this really hard to do.

Have you looked over Xnest - it's really powerful and can act as a server and a client. If remote boxes are ssh into the mac and using the multiple displays set up under Xnest your local display would be cluttered but one mac could support many remote machines with X11 services.

See these links for some good reading on the subject:
[Fun with Xnest HowTo|http://box.matto.nl/xnest.html]
[X11 for Mac OS X|http://www.scl.utah.edu/computers/mac/help/x11>

The only time I've seen this actually deployed, xnest was ditched after a few days of pain. Instead, a beefy Mac Pro with RAM/CPU to spare was set up with VMWare fusion and a virtual machine per user with linux/freeBSD installed. Then X11 could roam there free of "the dictator" known as Quartz Compositor.