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
A seamless web texture with illustration of pale color stains on canvas.
Source V. Hartikainen
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
Pixel by pixel, sharp and clean. Very light pattern with clear lines.
Source M.Ashok
This is so subtle I hope you can see it! Tweak at will.
Source Alexandre Naud
A seamless pattern formed from background pattern 102
Source Firkin
Prismatic Geometric Tessellation Pattern 3 No Background
Source GDJ
A tile-able background for websites with paper-like texture and a grid pattern layered on top of it.
Source V. Hartikainen
A simple but elegant classic. Every collection needs one of these.
Source Christopher Burton
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
A seamless chequerboard pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i. Alternative colour scheme.
Source Firkin
A background formed from an image of an old tile on the New York Metropolitan Museum of Art website. To get the base tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Prismatic Curved Diamond Pattern 4 No Background
Source GDJ
A blue gray fabric-like texture for websites. An yet another fabric-like texture. It has subtle vertical and diagonal stripes to it.
Source V. Hartikainen
One more from Badhon, sharp horizontal lines making an embossed paper feeling.
Source Badhon Ebrahim
A seamless web background with texture of aged grid paper.
Source V. Hartikainen
From a drawing in 'Hubert Montreuil, or the Huguenot and the Dragoon', Francisca Ouvry, 1873.
Source Firkin
Seamless Olive Green Web Background Image
Source V. Hartikainen