I skipped number 3, because it wasn’t all that great. Sorry.
Source Dima Shiper
Prismatic Geometric Pattern Background 2 No Black
Source GDJ
A seamless pattern formed from a tile made from page ornament 22. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Hypnotic Pattern No Background
Source GDJ
One more updated pattern. Not really carbon fiber, but it’s the most popular pattern, so I’ll give you an extra choice.
Source Atle Mo
An aged paper background tile with smeared and pressed text.
Source V. Hartikainen
Prismatic Abstract Background Design
Source GDJ
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
This background pattern contains a seamless texture of bark. It's not very realistic, but I think it looks quite nice.
Source V. Hartikainen
A repeating background of thick textured paper. Actually, it turned out to look like something between a paper and fabric.
Source V. Hartikainen
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Sounds French. Some 3D square diagonals, that’s all you need to know.
Source Graphiste
From a drawing in 'Resa i Afrika, genom Angola, Ovampo och Damaraland', P. Moller, 1899.
Source Firkin
Might not be super subtle, but quite original in its form.
Source Alex Smith
The image depicts a seamless pattern of a Japanese family crest called "chidori" in Japanese .A chidori in Japanese means a plover in English.
Source Yamachem
A seamless pattern based on a square tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
From a drawing in 'Cowdray: the history of a great English House', Julia Roundell, 1884.
Source Firkin
A huge one at 800x600px. Made from a photo I took going home after work.
Source Atle Mo
Prismatic Polka Dots Mark II No Background
Source GDJ
Zero CC tileable cork floor, photographed and made by me. CC0
Source Sojan Janso
New paper pattern with a slightly organic feel to it, using some thin threads.
Source Atle Mo