Not strictly seamless in that opposite edges are not identical. But they do marry up to make an interesting pattern
Source Firkin
The classic subtle pattern. Sort of wall/brick looking. Or moon-looking?
Source Joel Klein
Prismatic Triangular Background Design Mark II 5
Source GDJ
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
A blue background wallpaper for websites. It has a seamless texture with vertical stripes. It looks quite nice not only when using as a tiled background on websites, but also on computer desktops.
Source V. Hartikainen
Not the most creative name, but it’s a good all-purpose light background.
Source Dmitry
Medium gray pattern with small strokes to give a weave effect.
Source Catherine
Prismatic Rounded Squares Grid 3 No Background
Source GDJ
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
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
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
A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.
Source Firkin
A chequerboard pattern with a fruit theme. The fruits are from a posting by inkscapeforum.it.
Source Firkin
Prismatic Geometric Tessellation Pattern 2 No Background
Source GDJ
The tile this is based on can be retrieved by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Derived from an image that was uploaded to Pixabay by Darkmoon1968
Source Firkin
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Light and tiny, just the way you like it.
Source Rohit Arun Rao
The original enhanced with one of Inkscapes's filters.
Source Firkin
Prismatic Groovy Concentric Background 4 No Black
Source GDJ
Different from the original in being a simple tile stored as a pattern definition, rather than numerous repeated objects. Hence easy and quick to give this pattern to objects of different shapes. To get the tile in Inkscape, select the rectangle and use shift+alt+i.
Source Firkin
From an image on opengameart.org shared by rubberduck.
Source Firkin
From a drawing in 'Cassell's Library of English Literature', Henry Morley, 1883.
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