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 free seamless background with pink spots.
Source V. Hartikainen
Prismatic Geometric Pattern Background No Black
Source GDJ
Prismatic Floral Pattern 3 Variation 3 No Background
Source GDJ
More Japanese-inspired patterns, Gold Scales this time.
Source Josh Green
A gray background pattern with a texture of textile. Suits perfectly for web design.
Source V. Hartikainen
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
The following repeating website background is colored in a blue gray color and resembles a concrete wall or something similar to it.
Source V. Hartikainen
Remixed from a drawing in 'Incidents on a Journey through Nubia to Darfoor', F. Ensor, 1891.
Source Firkin
A grayscale fabric pattern with vertical lines of stitch holes.
Source V. Hartikainen
Remixed from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
A seamless light gray paper texture with horizontal double lines.
Source V. Hartikainen
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
Floral patterns might not be the hottest thing right now, but you never know when you need it!
Source Lauren
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Light gray version of the Binding pattern that looks a bit like fabric.
Source Newbury
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
An abstract texture of water. It's not perfect, but will do. You may download if you like it.
Source V. Hartikainen
Colour version of the original pattern.
Source Firkin