Basket Fibers, Basket Texture, Braid Background style CC0 texture.
Source 1A-Photoshop
A seamless pattern the starting point for which was a 'colour modulo' texture in Paint.net.
Source Firkin
Vector version of a JPG that was uploaded to Pixabay by theasad121
Source Firkin
The basic shapes never get old. Simple triangle pattern.
Source Atle Mo
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
To get the tile this is made up from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Otis Ray Redding was an American soul singer-songwriter, record producer, arranger, and talent scout. So you know.
Source Thomas Myrman
Super subtle indeed, a medium gray pattern with tiny dots in a grid.
Source Designova
A heavy dark gray base, some subtle noise and a 45-degree grid makes this look like a pattern with a tactile feel to it.
Source Atle Mo
Same as gray sand but lighter. A sandy pattern with small light dots, and some angled strokes.
Source Atle Mo
Some rectangles, a bit of dust and grunge, plus a hint of concrete.
Source Atle Mo
From a drawing in 'Hyde Park from Domesday-Book to date', John Ashton, 1896.
Source Firkin
Prismatic Groovy Concentric Background 4 No Black
Source GDJ
Derived from a PNG that was uploaded to Pixabay by nutkitten
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
Prismatic Abstract Background Design
Source GDJ
A seamless pattern the starting point for which was a 'colour modulo' texture in Paint.net.
Source Firkin
A bit strange this one, but nice at the same time.
Source Diogo Silva
Formed from a tile based on a drawing from 'Viaggi d'un artista nell'America Meridionale', Guido Boggiani, 1895.
Source Firkin
Like the name suggests, this background image consists of a pattern of dark bricks. It may be an option for you, if you are looking for something that looks like a brick wall for use as a background on web pages. It's not a masterpiece, but looks pretty nice when is tiled.
Source V. Hartikainen
ZeroCC tileable stone texture, edited from pixabay, CC0
Source Sojan Janso
A free grid paper background pattern for using on web sites.
Source V. Hartikainen
One more from Badhon, sharp horizontal lines making an embossed paper feeling.
Source Badhon Ebrahim
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
He influenced us all. “Don’t be sad because it’s over. Smile because it happened.”
Source Atle Mo
"Beige Stone", Tileable Texture.
Source V. Hartikainen