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
Hexagonal dark 3D pattern. What more can you ask for?
Source Norbert Levajsics
A dark pattern made out of 3×3 circles and a 1px shadow. This works well as a carbon texture or background.
Source Atle Mo
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
This one takes you back to math class. Classic mathematic board underlay.
Source Josh Green
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
This one is amazing, truly original. Go use it!
Source Viahorizon
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
This pattern comes in orange, and it looks as if it is "made of glass".
Source V. Hartikainen
A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
He influenced us all. “Don’t be sad because it’s over. Smile because it happened.”
Source Atle Mo
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin
Formed by heavily distorting part of a an image of a fish uploaded to Pixabay by GLady
Source Firkin
Black brick wall pattern. Brick your site up!
Source Alex Parker
Derived from a drawing in 'Elfrica. An historical romance of the twelfth century', Charlotte Boger, 1885
Source Firkin
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
Prismatic Curved Diamond Pattern 6 No Background
Source GDJ
Not the most creative name, but it’s a good all-purpose light background.
Source Dmitry
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin