Here are version 1 and version 2 of my 216-color palette arrangement:
Version 1 is used in Bryan Horling's Pixel Spy 1.3, a most excellent and vital utility for anyone working with computer graphics (and especially for Web work). I created version 2 because a)version 1 just wasn't pretty enough, and b)the minor mistake in the upper right irked me (slight discontinuity in the fourth row).
Despite the <Edit> button, the built-in palette editor is not as good as the one in ResEdit (and even that one leaves a bit to be desired), so I used a combination of Color It's image editor, ResEdit, and Pixel Spy to edit the palette.
As you may have surmised, I duplicated a few colors in version 2 for a more pleasing visual appearance. If you prefer non-duplicated colors, just use version 1 instead (I'll keep both versions available for downloading).
I don't have a Photoshop clut because Adobe uses a file format with which I am unfamiliar. If someone can provide me with the necessary technical info, I might "port" my palette. In the meantime, you could try Lynda's.