As far as fabric patterns goes, this is quite crisp.
Source Heliodor Jalba
Sharp pixel pattern, just like the good old days.
Source Paridhi
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
A lovely light gray pattern with stripes and a dash of noise.
Source V. Hartikainen
Zero CC tileable wood texture, made by me procedurally in Neo Texture Edit.
Source Sojan Janso
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Friend or Fortune? The story of a strange year', Robert Overton, 1897.
Source Firkin
A seamless pattern formed from a square tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-I.
Source Firkin
Prismatic Curved Diamond Pattern 8 No Background
Source GDJ
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i
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
Remixed from a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
Small dots with minor circles spread across to form a nice mosaic.
Source John Burks
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Derived from an image that was uploaded to Pixabay by Kaz
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Sort of like the Photoshop transparent background, but better!
Source Alex Parker
One more in the line of patterns inspired by Japanese/Asian styles. Smooth.
Source Kim Ruddock
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
Real snow that tiles, not easy. This is not perfect, but an attempt.
Source Atle Mo
From a drawing in 'Resa i Afrika, genom Angola, Ovampo och Damaraland', P. Moller, 1899.
Source Firkin
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
Background pattern made in "Grunge-Like" style. Available in both SVG and JPG formats. Edit to your needs then click the download button.
Source V. Hartikainen