From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Little x’es, noise and all the stuff you like. Dark like a Monday, with a hint of blue.
Source Tom McArdle
Remixed from a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin
Could be paper, could be a Polaroid frame – up to you!
Source Chaos
The basic shapes never get old. Simple triangle pattern.
Source Atle Mo
Same classic 45-degree pattern, dark version.
Source Luke McDonald
White fabric looking texture with some nice random wave features.
Source Hendrik Lammers
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
Prismatic Polyskelion Pattern No Background
Source GDJ
A free background image with a seamless texture of cardboard. This texture of cardboard looks quite realistic, especially when is actually tiled.
Source V. Hartikainen
More tactile goodness. This time in the form of some rough cloth.
Source Bartosz Kaszubowski
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
Looks like an old rug or a computer chip.
Source Patutin Sergey
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
The classic notebook paper with horizontal stripes.
Source Are Sundnes
From a design in 'Storia del Palazzo Vecchio in Firenze', Aurelio Gotti, 1889.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
This one needs to be used in small areas; you can see it repeat.
Source Luca