I skipped number 3, because it wasn’t all that great. Sorry.
Source Dima Shiper
Here's an yet another background for websites, with a seamless texture of wood planks this time.
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Prismatic Geometric Tessellation Pattern No Background
Source GDJ
The name tells you it has curves. Oh yes, it does!
Source Peter Chon
Alternative colour scheme. 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
Looks like an old rug or a computer chip.
Source Patutin Sergey
Formed by distorting a JPG from PublicDomainPictures
Source Firkin
Retro Circles Background 4 No Black
Source GDJ
Inspired by a drawing seen in 'City of Liverpool', James Picton, 1883.
Source Firkin
From a drawing in 'Hyde Park from Domesday-Book to date', John Ashton, 1896.
Source Firkin
Remixed from a drawing in 'Incidents on a Journey through Nubia to Darfoor', F. Ensor, 1891.
Source Firkin
One of the few full-color patterns here, but this one was just too good to pass up.
Source Alexey Usoltsev
Seamless Olive Green Web Background Image
Source V. Hartikainen
Remixed from a drawing that was uploaded to Pixabay by ractapopulous
Source Firkin
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin
First pattern tailor-made for Retina, with many more to come. All the old ones are upscaled, in case you want to re-download.
Source Atle Mo
One more in the line of patterns inspired by Japanese/Asian styles. Smooth.
Source Kim Ruddock
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin