This light blue background pattern is quite pleasing to the eye, it consists of a tiny rough grid pattern, which is seamless by design. That's it, if you like the color, you can use this seamless pattern in a web design without making any further modifications to it.
Source V. Hartikainen
Semi-light fabric pattern made out of random pixels in shades of gray.
Source Atle Mo
Based on several public domain drawings on Wikimedia Commons. This was formed from a rectangular tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i
Source Firkin
Prismatic Isometric Cube Wireframe Pattern No Background
Source GDJ
One more from Badhon, sharp horizontal lines making an embossed paper feeling.
Source Badhon Ebrahim
That’s what it is, a dark dot. Or sort of carbon looking.
Source Tsvetelin Nikolov
ZeroCC tileable moss texture, photographed and made by me. CC0
Source Sojan Janso
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
More tactile goodness. This time in the form of some rough cloth.
Source Bartosz Kaszubowski
Not so subtle. These tileable wood patterns are very useful.
Source Elemis
This one is super crisp at 2X. Lined paper with some dust and scratches.
Source HQvectors
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Small gradient crosses inside 45-degree boxes, or bigger crosses if you will.
Source Wassim
Abstract Stars Geometric Pattern Prismatic No Background
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
A dark striped seamless pattern suitable for use as a background on websites.
Source V. Hartikainen
A smooth mid-tone gray, or low contrast if you will, linen pattern.
Source Jordan Pittman
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin