From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Some more diagonal lines and noise, because you know you want it.
Source Atle Mo
A seamless pattern formed from miutopia mug remixes on a tablecloth.
Source Firkin
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
Geometric triangles seem to be quite hot these days.
Source Pixeden
A free seamless background texture of "timber wall" (colored in dark brown).
Source V. Hartikainen
Tweed is back in style – you heard it here first. Also, the @2X version here is great!
Source Simon Leo
Prismatic Hexagonalism Pattern No Background
Source GDJ
Number five from the same submitter, makes my job easy.
Source Dima Shiper
Prismatic Geometric Tessellation Pattern No Background
Source GDJ
Geometric lines are always hot, and this pattern is no exception.
Source Listvetra
A seamless texture of black leather. I think it will look best when used in headers, footers or sidebars.
Source V. Hartikainen
Textured Red Brown Plastic, Free Background Pattern. Although there's already enough plastic in our lives, let's bring it to the web too.)
Source V. Hartikainen
Can’t believe we don’t have this in the collection already! Slick woven pattern with crisp details.
Source Max Rudberg
A pale olive green background with a seamless texture.
Source V. Hartikainen
Zero CC tileable Crackled Cement (streaks) texture, photographed and made by me. CC0
Source Sojan Janso
Snap! It’s a pattern, and it’s not grayscale! Of course you can always change the color in Photoshop.
Source Atle Mo
Here's a seamless brown cork board background texture. Feel free to download or reshare if you like.
Source V. Hartikainen
It’s like Shine Dotted’s sister, only rotated 45 degrees.
Source mediumidee
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin