Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Background formed from the original with an emboss effect
Source GDJ
I love these crisp, tiny, super subtle patterns.
Source Badhon Ebrahim
Dark squares with some virus-looking dots in the grid.
Source Hugo Loning
As far as fabric patterns goes, this is quite crisp.
Source Heliodor Jalba
Some more diagonal lines and noise, because you know you want it.
Source Atle Mo
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
Colour version of the original seamless pattern.
Source Firkin
All good things come in threes, so I give you the third in my little concrete wall series.
Source Atle Mo
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
This background texture resembles stone. It may be used as a background on web pages or on some of their html elements (header, borders, menu bar, etc.). Just modify it for your needs.
Source V. Hartikainen
A free background tile with a pattern of pink bump dots. This background tile is sweet! Moreover, it's designed for use as website backgrounds.
Source V. Hartikainen
Remixed from a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
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
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Sort of like the Photoshop transparent background, but better!
Source Alex Parker
Zero CC tileable bark texture, photographed and made by me. CC0
Source Sojan Janso