Carbon Fiber v2@2X #106
 Carbon  CC BY-SA 3.0

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

 More Textures
Background pattern 259 (colour 6) #2097
 Blue  CC 0

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

Light Orange Brown Wallpaper #911
 Stripes  CC BY-SA 3.0

A free light orange brown wallpaper with vertical stripes designed for use as a tiled background on websites. An yet another background pattern with vertical stripes.

Source V. Hartikainen

Background pattern 215 #2371
 Brown  CC 0

A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.

Source Firkin

Green Fibers@2X #92
 Dark  CC BY-SA 3.0

The green fibers pattern will work very well in grayscale as well.

Source Matteo Di Capua

Carbon Fiber #3
 Carbon  CC BY-SA 3.0

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

ed62's pattern remixed #1728
 Dark  CC 0

The original has been presented as black on transparent and stored in the pattern definitions. To retrieve the unit tile select the rectangle in Inkscape and use shift+alt+i

Source Firkin

Background pattern 270 #2061
 Dark  CC 0

A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i

Source Firkin

Wallpaper Tile 13 #240
 Light  CC 0

An abstract Background pattern of purple twisty patterns.

Source TikiGiki

Fake Brick #358
 Dark  CC BY-SA 3.0

Black, simple, elegant, and useful.

Source Marat

Seamless tile 4 #1812
 Red  CC 0

Not strictly seamless in that opposite edges are not identical. But they do marry up to make an interesting pattern

Source Firkin