I took the liberty of using Dmitry’s pattern and made a version without perforation.
Source Atle Mo
Inspired by a 1930s wallpaper pattern I saw on TV.
Source Firkin
The basic shapes never get old. Simple triangle pattern.
Source Atle Mo
Remixed from a design seen on Pixabay. The basic tile can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A free seamless background image with a texture of dark red "canvas". It should look very nice on web sites.
Source V. Hartikainen
Prismatic Abstract Geometric Background 2 No Black
Source GDJ
A free grid paper background pattern for using on web sites.
Source V. Hartikainen
White circles connecting on a light gray background.
Source Mark Collins
From a drawing in 'Cowdray: the history of a great English House', Julia Roundell, 1884.
Source Firkin
Your eyes can trip a bit from looking at this – use it wisely.
Source Michal Chovanec
This background pattern contains a seamless texture of bark. It's not very realistic, but I think it looks quite nice.
Source V. Hartikainen
From a drawing in 'The Quiver of Love', Walter Crane, 1876
Source Firkin
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
Prismatic Geometric Tessellation Pattern 3 No Background
Source GDJ
A beautiful dark padded pattern, like an old classic sofa.
Source Chris Baldie
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Colourful background achieved with gradient fills.
Source Firkin
A seamless pattern from a tile made from a jpg on Pixabay. To get the tile select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
The name Paisley reminds me of an old British servant. That’s just me.
Source Swetha
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
An emulated “transparent” background pattern, like that of all kinds of computer graphics software.
Source AdamStanislav
Fake or not, it’s quite luxurious.
Source Factorio.us Collective
Used a cherry by doctormo to make this seamless pattern
Source Firkin