The image depicts a Japanese Edo pattern called "kanoko or 鹿の子" meaning "fawn" which has a fur with small white spots.
Source Yamachem
The image depicts a seamless pattern of pine tree leaves.
Source Yamachem
This one resembles a black concrete wall when is tiled. It should look great, at least with dark website themes.
Source V. Hartikainen
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
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
From a drawing in 'Studies for Stories', Jean Ingelow, 1864.
Source Firkin
This light yellow background pattern consists of an irregular pattern of spots. Here's a light background pattern with yellowish tint.
Source V. Hartikainen
Seamless tile drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
First pattern tailor-made for Retina, with many more to come. All the old ones are upscaled, in case you want to re-download.
Source Atle Mo
Seamless pattern formed from a tile that can be extracted by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
A seamless pattern based on a rectangular tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
The edges of all the red objects line up either vertically or horizontally, but it doesn't appear so. Made from a square tile that can be got by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Prismatic Polka Dots Mark II No Background
Source GDJ
Prismatic Curved Diamond Pattern 4 No Background
Source GDJ
Derived from a drawing in 'The Murmur of the Shells', Samuel Cowen, 1879.
Source Firkin
From a drawing in 'Uit de geschiedenis der Heilige Stede te Amsterdam', Yohannes Sterck, 1898.
Source Firkin
Nice and simple crossed lines in dark gray tones.
Source Stefan Aleksić
Prismatic Groovy Concentric Background 2 No Black
Source GDJ
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Feel free to use this seamless background texture as a background on a web site. It's colored in a light pink color and is seamlessly tile-able.
Source V. Hartikainen
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight