Fabric-ish patterns are close to my heart. French Stucco to the rescue.
Source Christopher Buecheler
Tile available in Inkscape using shift-alt-i on the selected rectangle
Source Firkin
A good starting point for a cardboard pattern. This would work well in a variety of colors.
Source Atle Mo
Submitted in a cream color, but you know how I like it.
Source Devin Holmes
More Japanese-inspired patterns, Gold Scales this time.
Source Josh Green
A seamless pattern with a unit cell drawn as a bitmap in Paint.net and vectorized in Vector Magic.
Source Firkin
You know, tiny and sharp. I’m sure you’ll find a use for it.
Source Atle Mo
You may use it as is, or modify it as you like.
Source V. Hartikainen
Nicely executed tiling for an interesting pattern.
Source Ignasi Àvila Padró
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
A version without colours blended together to give a different look.
Source Firkin
Prismatic Polka Dots Mark II 2 No Background
Source GDJ
Prismatic Hypnotic Pattern 2 No Background
Source GDJ
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
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
Sounds like something from World of Warcraft. Has to be good.
Source Tony Kinard
Colorful Floral Background 3 No Black
Source GDJ
The image depicts a seamless pattern of pine tree leaves.
Source Yamachem
From a drawing in 'Artists and Arabs', Henry Blackburn, 1868
Source Firkin
This is the third pattern called Dark Denim, but hey, we all love them!
Source Brandon Jacoby