This one is quite simple in design, it consists of vertical stripes layered on top of a seamless texture.
Source V. Hartikainen
A seamless web background with texture of aged grid paper.
Source V. Hartikainen
This one takes you back to math class. Classic mathematic board underlay.
Source Josh Green
Background Wall, Art Abstract, Star Well & CC0 texture.
Source Ractapopulous
Here is a new seamless wood texture for using as blog or website backgrounds.
Source V. Hartikainen
From a drawing in 'Navigations de Alouys de Cademoste.-La Navigation du Capitaine Pierre Sintre', Alvise da ca da Mosto, 1895.
Source Firkin
You know, tiny and sharp. I’m sure you’ll find a use for it.
Source Atle Mo
This is the remix of "Strawberry Pattern Background" uploaded by "GDJ". Thanks. I realigned strawberries so as to get seamless and changed the BG color.
Source Yamachem
An abstract texture of water. It's not perfect, but will do. You may download if you like it.
Source V. Hartikainen
Just to prove my point, here is a slightly modified dark version.
Source Atle Mo
Prismatic Snowflakes Pattern 2 No Background
Source GDJ
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Black And White Floral Pattern Background from PDP.
Source GDJ
Dark, lines, noise, tactile. You get the drift.
Source Anatoli Nicolae
Pattern #100! A black classic knit-looking pattern.
Source Factorio.us Collective
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
Remixed from a drawing in 'Paul's Sister', Frances Peard, 1889.
Source Firkin
A free green background pattern with a pattern of rhombuses on a seamless texture. Feel free to use it as a tiled background image on your web site.
Source V. Hartikainen
This is a semi-dark pattern, sort of linen-y.
Source Sagive SEO
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
Prismatic Geometric Tessellation Pattern 4 No Background
Source GDJ