Here's a quite bright pink background pattern for use on websites. It doesn't look like a real fur, but it definitely resembles one.
Source V. Hartikainen
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Prismatic Isometric Cube Extra Pattern No Background
Source GDJ
This was submitted in a beige color, hence the name. Now it’s a gray paper pattern.
Source Konstantin Ivanov
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Square design drawn in Paint.net and vectorized in Vector Magic.
Source Firkin
Zero CC tileable wood texture, made by me procedurally in Neo Texture Edit.
Source Sojan Janso
Fix and cc0 to get the tile this is based on.
Source SliverKnight
Prismatic Abstract Background Design No Black
Source GDJ
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i
Source Firkin
Not strictly seamless in that opposite edges are not identical. But they do marry up to make an interesting pattern
Source Firkin
Bright Multicolored Floral Background by Karen Arnold from PDP.
Source GDJ
If you need a green background for your blog/website, try this one. Remember that Green Striped Background is seamlessly tileable.
Source V. Hartikainen
Might not be super subtle, but quite original in its form.
Source Alex Smith
A simple example on using clones. You can generate a nice base for a pattern fill quickly with it.
Source Lazur URH
Embossed lines and squares with subtle highlights.
Source Alex Parker
A fun-looking elastoplast/band-aid pattern. A hint of orange tone in this one.
Source Josh Green
Sweet and subtle white plaster with hints of noise and grunge.
Source Phil Maurer
From a drawing in 'Friend or Fortune? The story of a strange year', Robert Overton, 1897.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Everyone needs some stardust. Sprinkle it on your next project.
Source Atle Mo
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
From a drawing in 'Studies for Stories', Jean Ingelow, 1864.
Source Firkin
Because I love dark patterns, here is Brushed Alum in a dark coating.
Source Tim Ward