If you need a green background for your blog/website, try this one. Remember that Green Striped Background is seamlessly tileable.
Source V. Hartikainen
The first pattern on here using opacity. Try it on a site with a colored background, or even using mixed colors.
Source Nathan Spady
One more from Badhon, sharp horizontal lines making an embossed paper feeling.
Source Badhon Ebrahim
Utilising a bird from s-light and some flowers from Almeidah. To get the unit tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
A seamless pattern formed from a sports car on clker.com. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
You know I’m a sucker for these. Well-crafted paper pattern.
Source Mihaela Hinayon
More in the paper realm, this time with fibers.
Source Jorge Fuentes
ZeroCC tileable stone texture, edited from pixabay, CC0
Source Sojan Janso
As far as fabric patterns goes, this is quite crisp.
Source Heliodor Jalba
Remixed from a drawing in 'A Child of the Age', Francis Adams, 1894.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
From a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
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
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
There are many carbon patterns, but this one is tiny.
Source Designova
This is a seamless pattern which is derived from a flower petal image.
Source Yamachem
Heavily remixed from a drawing in 'Barbara Leybourne; a story of eighty years ago', Sarah Hamer, 1889.
Source Firkin
This is the remix of "polka dot seamless pattern".The image depicts polka dot seamless pattern.
Source Yamachem
From a drawing in 'Resa i Afrika, genom Angola, Ovampo och Damaraland', P. Moller, 1899.
Source Firkin
A seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin
Prismatic Geometric Pattern Variation 2 With Background
Source GDJ
This one takes you back to math class. Classic mathematic board underlay.
Source Josh Green