A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Abstract Arbitrary Geometric Background derived from an image on Pixabay.
Source GDJ
From a drawing in 'Worsborough; its historical associations and rural attractions', Joseph Wilkinson, 1879.
Source Firkin
Utilising some flowers from Almeidah. To get the unit tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.
Source Firkin
Like the name suggests, this background image consists of a pattern of dark bricks. It may be an option for you, if you are looking for something that looks like a brick wall for use as a background on web pages. It's not a masterpiece, but looks pretty nice when is tiled.
Source V. Hartikainen
Luxurious looking pattern (for a T-shirt maybe?) with a hint of green.
Source Simon Meek
A dark gray, sandy pattern with small light dots, and some angled strokes.
Source Atle Mo
These dots are already worn for you, so you don’t have to.
Source Matt McDaniel
A dark pattern made out of 3×3 circles and a 1px shadow. This works well as a carbon texture or background.
Source Atle Mo
Prismatic Polka Dots Mark II No Background
Source GDJ
Remixed from a drawing in 'An Index to Deering's Nottinghamia Vetus et Nova', Rupert Chicken, 1899. The unit tile can be had by selecting the rectangle in Inkscape and using shift-alt-i
Source Firkin
Geometric triangles seem to be quite hot these days.
Source Pixeden
An interesting dark spotted pattern at an angle.
Source Hendrik Lammers
This was formed by distorting an image of a background on Pixabay.
Source Firkin
Love me some light mesh on a Monday. Sharp.
Source Wilmotte Bastien
ZeroCC tileable mossy (lichen) stone texture, edited from pixabay. CC0
Source Sojan Janso
This one is something special. I’d call it a flat pattern, too. Very well done, sir!
Source GetDiscount
A free tileable background colored in off-white (antique white) color.
Source V. Hartikainen
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
A seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin
Inspired by this, I came up with this pattern. Madness!
Source Atle Mo