A seamless gray background texture suitable for use on websites. To me, it has the look of stone. Feel free to modify it to meet your needs (by making it a bit lighter or darker, for example).
Source V. Hartikainen
This one needs to be used in small areas; you can see it repeat.
Source Luca
A chequerboard pattern with a fruit theme. The fruits are from a posting by inkscapeforum.it.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Prismatic Curved Diamond Pattern 5 No Background
Source GDJ
One more sharp little tile for you. Subtle circles this time.
Source Blunia
This one takes you back to math class. Classic mathematic board underlay.
Source Josh Green
Not even 1kb, but very stylish. Gray thin lines.
Source Struck Axiom
Plywood Web Background background image for use in web design.
Source V. Hartikainen
Background Wall, Art Abstract, white Well & CC0 texture.
Source Ractapopulous
Inspired by a pattern seen on a public domain image of a very old tile. To get the unit cell, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Abstract Geometric Background 5 No Black
Source GDJ
An aged paper background tile with smeared and pressed text.
Source V. Hartikainen
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Hexagonal dark 3D pattern. What more can you ask for?
Source Norbert Levajsics
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
Light honeycomb pattern made up of the classic hexagon shape.
Source Federica Pelzel
An alternative colour scheme to the original seamless pattern.
Source Firkin
Just to prove my point, here is a slightly modified dark version.
Source Atle Mo
Prismatic Groovy Concentric Background 5
Source GDJ
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Tiny little flowers growing on your screen. Nice, huh?
Source Themes Tube
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Dare I call this a «flat pattern»? Probably not.
Source Dax Kieran