You guessed it – looks a bit like cloth.
Source Peax Webdesign
A floral background formed from numerous clones of flower 117.
Source Firkin
Dark, crisp and subtle. Tiny black lines on top of some noise.
Source Wilmotte Bastien
A seamlessly tileable pink background texture.
Source V. Hartikainen
If you like it a bit trippy, this wave pattern might be for you.
Source Ian Soper
Alternative colour scheme. 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
Geometric lines are always hot, and this pattern is no exception.
Source Listvetra
A dark background pattern/texture of a dimpled metal plate.
Source V. Hartikainen
From a drawing in 'Uit de geschiedenis der Heilige Stede te Amsterdam', Yohannes Sterck, 1898.
Source Firkin
The classic 45-degree diagonal line pattern, done right.
Source Jorick van Hees
A seamless pattern formed from cross 4. To get the original tile select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
From a drawing in 'La Principauté de Liège et les Pays-Bas au XVIe siècle', Société des Bibliophiles Liégeois ,1887.
Source Firkin
A seamless canvas texture for using as background on websites. Colored in pale tones of brown.
Source V. Hartikainen
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
The image depicts a seamless pattern of a tortoise in tortoiseshell (hexagon).
Source Yamachem
Green Background Pattern
Source V. Hartikainen
A pattern formed from a squared tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
This one takes you back to math class. Classic mathematic board underlay.
Source Josh Green
A dark striped seamless pattern suitable for use as a background on websites.
Source V. Hartikainen
Here's a new paper-like background for free use on personal and commercial projects (this applies to all background patterns here).
Source V. Hartikainen
More tactile goodness. This time in the form of some rough cloth.
Source Bartosz Kaszubowski
A repeating background of thick textured paper. Actually, it turned out to look like something between a paper and fabric.
Source V. Hartikainen