The first pattern on here using opacity. Try it on a site with a colored background, or even using mixed colors.
Source Nathan Spady
Sweet and subtle white plaster with hints of noise and grunge.
Source Phil Maurer
The basic shapes never get old. Simple triangle pattern.
Source Atle Mo
Remixed from a drawing in 'The March of Loyalty', Letitia MacClintock, 1884.
Source Firkin
Prismatic Groovy Concentric Background 5
Source GDJ
Remixed from a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
From a drawing in 'Royal Ramsgate', James Simson, 1897.
Source Firkin
A rusty grunge background for websites. Feel free to use it in your site's theme.
Source V. Hartikainen
A seamless pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
Sort of like the Photoshop transparent background, but better!
Source Alex Parker
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
A yellow tiled background... Blurriness, bokeh effect and rectangles pattern in one mix.
Source V. Hartikainen
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
A frame using leaves from an image that was uploaded to Pixabay by mayapujiati
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Remixed from a PNG that was uploaded to Pixabay by VictorianLady
Source Firkin
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
That’s what it is, a dark dot. Or sort of carbon looking.
Source Tsvetelin Nikolov