Access X windows on Linux from Mac and vice versa

Conversely, is it possible to connect Mac X11 from Linux?

Do you mean use your Linux machine to view/control X11 applications running on your Mac?
Sure. That's standard X11.

If you're expecting to see the whole Mac GUI, or even control individual Mac applications, then no - the standard Mac desktop uses Aqua, not X11 for its window management. You would be able to control X11-based apps, but that is not the majority of Mac applications.

If it is control of the Mac UI that you're after, the closest you'd get is VNC which acts as a full-screen system that lets you see (and control) the entire Mac desktop, doing anything that a user could do sitting at the local keyboard and mouse.
Bear in mind, though, that you wouldn't have a separate desktop for the VNC user - the VNC screen would mimic whatever the machine is doing, potentially interrupting the keyboard and mouse usage of whoever was using the machine.

To go from your mac to a Linux box you want to:

1. Start X11.app

2. From the X11 terminal, or standard terminal enter

3. ssh -Y <hostname or IP address> and log in.

4. run your desired command.

Displaying X windows back to the mac works really well. From the mac:

ssh -X <linux hostname>

I've not yet had a reason to display an X window from the mac to an linux box.

And as was written previously, VNC is very useful, I use Chicken of the VNC.

Another way,

http://www.nomachine.com/

this though will only allow you to display the Linux desktop to you mac. it works really well. even over long distances (between Wisconsin and Georiga).