An abstract Background pattern of purple twisty patterns.
Source TikiGiki
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
Same as Silver Scales, but in black. Turn your site into a dragon with this great scale pattern.
Source Alex Parker
Some more diagonal lines and noise, because you know you want it.
Source Atle Mo
Prismatic Geometric Pattern Background 2 No Black
Source GDJ
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin
Tiny little flowers growing on your screen. Nice, huh?
Source Themes Tube
From a design found in 'History of the Virginia Company of London; with letters to and from the first Colony, never before printed', Edward Neill, 1869.
Source Firkin
Prismatic Polka Dots Mark II 3 No Background
Source GDJ
Got some felt in my mailbox today, so I scanned it for you to use.
Source Atle Mo
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
Here's an yet another background for websites, with a seamless texture of wood planks this time.
Source V. Hartikainen
Pattern #100! A black classic knit-looking pattern.
Source Factorio.us Collective
A slightly grainy paper pattern with small horizontal and vertical strokes.
Source Atle Mo
Background Wall, Art Abstract, Star Well & CC0 texture.
Source Ractapopulous
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
Prismatic Geometric Pattern Variation 2 With Background
Source GDJ
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A seamless paper background colored in pale yellow.
Source V. Hartikainen
I know there is one here already, but this is sexy!
Source Gjermund Gustavsen
This one has rusty dark brown texture.
Source V. Hartikainen
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i
Source Firkin