Scanned some rice paper and tiled it up for you. Enjoy.
Source Atle Mo
Geometric lines are always hot, and this pattern is no exception.
Source Listvetra
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
Zero CC tileable Crackled Cement (streaks) texture, photographed and made by me. CC0
Source Sojan Janso
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
Super detailed 16×16 tile that forms a beautiful pattern of straws.
Source Pavel
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Prismatic Rounded Squares Grid 4 No Background
Source GDJ
A repeating background of beige paper with vintage look. Repeats to infinity, as usual.
Source V. Hartikainen
A seamless pattern formed from a square tile. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Floral Pattern 3 Variation 3 No Background
Source GDJ
I know there is one here already, but this is sexy!
Source Gjermund Gustavsen
A seamless chequerboard pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i. Alternative colour scheme.
Source Firkin
ZeroCC tileabel stone granite texture, edited from pixabay. CC0
Source Sojan Janso
From a drawing in 'Jardyne's Wife', Charles Wills, 1891.
Source Firkin
Could be paper, could be a Polaroid frame – up to you!
Source Chaos
Here's an yet another seamless note paper texture for use as a background on websites.
Source V. Hartikainen
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin
A very dark spotted twinkle pattern for your twinkle needs.
Source Badhon Ebrahim
From a drawing in 'Royal Ramsgate', James Simson, 1897.
Source Firkin
A free seamless background texture of "timber wall" (colored in dark brown).
Source V. Hartikainen
Looks like a technical drawing board: small squares forming a nice grid.
Source We Are Pixel8
A smooth mid-tone gray, or low contrast if you will, linen pattern.
Source Jordan Pittman
I love cream! 50x50px and lovely in all the good ways.
Source Thomas Myrman