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
Dead simple but beautiful horizontal line pattern.
Source Fabian Schultz
A light gray background pattern with seamless fabric-like texture and almost unnoticeable stripes.
Source V. Hartikainen
This is the remix of an Openclipart clipart called "Maze" uploaded by "any_ono_mous".Thanks.This is a seamless pattern of a maze.
Source Yamachem
Number 1 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
A background pattern inspired by designs seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
Super subtle indeed, a medium gray pattern with tiny dots in a grid.
Source Designova
Prismatic Geometric Pattern Background No Black
Source GDJ
Simple wide squares with a small indent. Fits all.
Source Petr Šulc.
A brown seamless wood texture in a form of stripe pattern. The result has turned out pretty well, in my opinion.
Source V. Hartikainen
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Floral patterns might not be the hottest thing right now, but you never know when you need it!
Source Lauren
Brushed aluminum, in a bright gray version. Lovely 2X as well.
Source Andre Schouten
The first pattern on here using opacity. Try it on a site with a colored background, or even using mixed colors.
Source Nathan Spady
Prismatic Rounded Squares Grid 3 No Background
Source GDJ
Simple wide squares with a small indent. Fits all.
Source Petr Šulc.
Looks like an old rug or a computer chip.
Source Patutin Sergey
A gray background pattern with a texture of textile. Suits perfectly for web design.
Source V. Hartikainen
Dark squares with some virus-looking dots in the grid.
Source Hugo Loning
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A seamless pattern of leopard skin. It should look nice as a background element on web pages.
Source V. Hartikainen
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857
Source Firkin
Abstract Ellipses Background Grayscale
Source GDJ
Prismatic Geometric Pattern Background 2 No Black
Source GDJ