I skipped number 3, because it wasn’t all that great. Sorry.
Source Dima Shiper
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
From a drawing in 'Resa i Afrika, genom Angola, Ovampo och Damaraland', P. Moller, 1899.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Remixed from a JPG that was uploaded to Pixabay by susanlu4esm
Source Firkin
From a drawing in 'Artists and Arabs', Henry Blackburn, 1868
Source Firkin
Some rectangles, a bit of dust and grunge, plus a hint of concrete.
Source Atle Mo
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 light background pattern with diagonal stripes. Here's a simple light striped background for you.
Source V. Hartikainen
Light gray grunge wall with a nice texture overlay.
Source Adam Anlauf
Zero CC tileable wood texture, made by me procedurally in Neo Texture Edit.
Source Sojan Janso
This background pattern looks like bamboo to me. Feel free to download it for your website (for your blog perhaps?).
Source V. Hartikainen
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
A seamless paper background texture colored in pale yellow. This seamless texture is ideal for those who need a yellow background image for their website. The texture resembles paper.
Source V. Hartikainen
Formed by distorting the inside front cover of 'Diversæ insectarum volatilium : icones ad vivum accuratissmè depictæ per celeberrimum pictorem', Jacob Hoefnagel, 1630.
Source Firkin
From a drawing in 'Heroes of North African Discovery', Nancy Meugens, 1894.
Source Firkin
It almost looks a bit blurry, but then again, so are fishes.
Source Petr Šulc
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
Inspired by a design found in 'Konstantinápolyi emlékeim', Miklos Chriszto, 1893.
Source Firkin
Remixed from a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
New paper pattern with a slightly organic feel to it, using some thin threads.
Source Atle Mo