Light square grid pattern, great for a “DIY projects” sort of website, maybe?
Source Rafael Almeida
Prismatic Geometric Pattern Variation 2 With Background
Source GDJ
Washi (和紙?) is a type of paper made in Japan. Here’s the pattern for you!
Source Carolynne
Drawn in Paint.net using the kaleidoscope plug-in and vectorised.
Source Firkin
This one has rusty dark brown texture.
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 pattern with green and yellow diagonal lines on top of a white dotted background.
Source V. Hartikainen
Vertical lines with a bumpy, yet crisp, feel to it.
Source Raasa
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
If you’re sick of the fancy 3D, grunge and noisy patterns, take a look at this flat 2D brick wall.
Source Listvetra
Derived from an image that was uploaded to Pixabay by Darkmoon1968
Source Firkin
Prismatic Groovy Concentric Background 2
Source GDJ
A seamless pattern of dark bricks. Maybe it's not very realistic, but it looks good in my opinion.
Source V. Hartikainen
Dare I call this a «flat pattern»? Probably not.
Source Dax Kieran
Super simple but very nice indeed. Gray with vertical stripes.
Source Merrin Macleod
Alternative colour scheme for the original floral pattern.
Source Firkin
Here's an yet another seamless note paper texture for use as a background on websites.
Source V. Hartikainen
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Inspired by a 1930s wallpaper pattern I saw on TV.
Source Firkin
It’s an egg, in the form of a pattern. This really is 2012.
Source Paul Phönixweiß
This one is amazing, truly original. Go use it!
Source Viahorizon