With the recent iOS 5 and OS X Lion updates I’ve been noticing a lot more linen in my UI. It shows up everywhere, from the login screen in Lion to the canvas behind a Safari window on the iPad and OS X.
I was curious to find out where it appears and discovered this thread on reddit.
I discovered at least 4 different shades.

Dock.app – backgroundTile.png
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Dock.app – defaultdesktop.png
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AppKit.framework – NSLinenBackgroundPattern.png

Safari.framework – ReadingList-BGLinen.png
It’s interesting that the Reading List variant isn’t 256px by 256px, but rather 300px by 300px – a non base-two size. It’s also worth noting that the iPad uses the darkest texture for the canvas in Safari, while Lion uses the second lightest version.
Update: George mentions in the comments, as of 10.7.3 backgroundTile.png from the Dock.app bundle was renamed to ecsb_background_tile.png. The files appear to be exactly the same.
Update 2: The new beta of Messages for Mountain Lion includes a new addition to the linen family.
/Applications/iChat.app/Contents/Resources/linen.tiff