Sometimes you just need the simplest thing.
Source Fabricio
A free seamless background image with a texture of dark red "canvas". It should look very nice on web sites.
Source V. Hartikainen
It’s okay to be square! A nice light gray pattern with random squares.
Source Waseem Dahman
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
A white version of the very popular linen pattern.
Source Ant Ekşiler
8 by 8 pixels, and just what the title says.
Source pixilated
From a drawing in 'Cowdray: the history of a great English House', Julia Roundell, 1884.
Source Firkin
Prismatic Groovy Concentric Background 2
Source GDJ
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
To get the tile this is made up from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
Number five from the same submitter, makes my job easy.
Source Dima Shiper
Derived from an image that was uploaded to Pixabay by TheDigitalArtist
Source Firkin
A smooth mid-tone gray, or low contrast if you will, linen pattern.
Source Jordan Pittman
Continuing the geometric trend, here is one more.
Source Mike Warner
From a drawing in 'Az Osztrák-Magyar Monarchia irásban és képben', 1885.
Source Firkin
This was formed by distorting an image of a background on Pixabay.
Source Firkin
Here's a bluish gray striped background pattern for use on web sites.
Source V. Hartikainen
Derived from an image that was uploaded to Pixabay by mdmelo.
Source Firkin
This is a grid, only it’s noisy. You know. Reminds you of those printed grids you draw on.
Source Vectorpile
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Prismatic Polka Dots Mark II 3 No Background
Source GDJ