Simple gray checkered lines, in light tones.
Source Radosław Rzepecki
An alternative colour scheme for the original seamless texture formed from an image on Pixabay.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Small gradient crosses inside 45-degree boxes, or bigger crosses if you will.
Source Wassim
Prismatic Abstract Background Design No Black
Source GDJ
Sharp but soft triangles in light shades of gray.
Source Pixeden
Inspired by a drawing seen in 'City of Liverpool', James Picton, 1883.
Source Firkin
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
A seamless pattern with wide vertical stripes colored in pale yellow.
Source V. Hartikainen
Sharp pixel pattern looking like some sort of fabric.
Source Dmitry
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
This was formed by distorting an image of a background on Pixabay.
Source Firkin
It’s okay to be square! A nice light gray pattern with random squares.
Source Waseem Dahman
A background pattern inspired by designs seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
Wasn't satisfied with the original's colouring. Too much component transfer and colormatrixes yet the results are lacking a bit. So this time it is a simple black to transparent fade, making it possible remixing easily once there will be other blending modes supported as well. Probably in inkscape 0.92.
Source Lazur URH
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Just to prove my point, here is a slightly modified dark version.
Source Atle Mo
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
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
Seamless Green Tile Background
Source V. Hartikainen