Simple gray checkered lines, in light tones.
Source Radosław Rzepecki
Prismatic Basic Pattern 2 No Background
Source GDJ
The image is a remix of "edo pattern-samekomon".I changed the color of dots from black to white and added BG in light-brown.
Source Yamachem
Not the most creative name, but it’s a good all-purpose light background.
Source Dmitry
Remixed from a JPG that was uploaded to Pixabay by theasad121
Source Firkin
Prismatic Snowflakes Pattern No Background
Source GDJ
Prismatic Geometric Pattern Background 2 No Black
Source GDJ
From a drawing in 'Kingsdene', Maria Fetherstonehaugh, 1878.
Source Firkin
Geometric triangles seem to be quite hot these days.
Source Pixeden
By popular request, an outline version of the pentagon pattern.
Source Atle Mo
Could remind you a bit of those squares in Super Mario Bros, yeh?
Source Jeff Wall
Remixed from a design seen on Pixabay. The basic tile can be had by selecting the rectangle in Inkscape and using shift+alt+i
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
All good things come in threes, so I give you the third in my little concrete wall series.
Source Atle Mo
Light square grid pattern, great for a “DIY projects” sort of website, maybe?
Source Rafael Almeida
A seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin
Tile available in Inkscape using shift-alt-i on the selected rectangle
Source Firkin
Prismatic Geometric Tessellation Pattern 3 No Background
Source GDJ
You know I love paper patterns. Here is one from Stephen. Say thank you!
Source Stephen Gilbert
One of the few full-color patterns here, but this one was just too good to pass up.
Source Alexey Usoltsev
Hey, you never know when you’ll need a bird pattern, right?
Source Pete Fecteau
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Zero CC tileable moss or lichen covered stone texture, edited from pixabay. CC0
Source Sojan Janso
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