A comeback for you: the popular Escheresque, now in black.
Source Patten
A very dark spotted twinkle pattern for your twinkle needs.
Source Badhon Ebrahim
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Dark blue concrete wall with some small dust spots.
Source Atle Mo
A slightly more textured pattern, medium gray. A bit like a potato sack?
Source Bilal Ketab
Looks like an old wall. I guess that’s it then?
Source Viahorizon
Retro Circles Background 7 No Black
Source GDJ
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Prismatic Geometric Tessellation Pattern 4 No Background
Source GDJ
A free background pattern with abstract green tiles.
Source V. Hartikainen
Prismatic Polka Dots Mark II No Background
Source GDJ
Number 4 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
This pattern comes in orange, and it looks as if it is "made of glass".
Source V. Hartikainen
Feel free to download this "Dark Wood" background texture for your web site. The background tiles seamlessly!
Source V. Hartikainen
Utilising some flowers from Almeidah. To get the unit tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Might not be super subtle, but quite original in its form.
Source Alex Smith
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A black tile-able background with paper-like texture.
Source V. Hartikainen
Inspired by a design found in 'Konstantinápolyi emlékeim', Miklos Chriszto, 1893.
Source Firkin
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