Not strictly seamless in that opposite edges are not identical. But they do marry up to make an interesting pattern
Source Firkin
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Inspired by a design found in 'Konstantinápolyi emlékeim', Miklos Chriszto, 1893.
Source Firkin
The classic notebook paper with horizontal stripes.
Source Are Sundnes
Prismatic Rounded Squares Grid 4 No Background
Source GDJ
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
This background pattern looks like bamboo to me. Feel free to download it for your website (for your blog perhaps?).
Source V. Hartikainen
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Derived from an image that was uploaded to Pixabay by mdmelo.
Source Firkin
This is a more minute version of "fishnet 01".The image depicts a seamless pattern of a fishnet with a plenty of fish.It may be a lucky charm for fishermen.
Source Yamachem
Pattern Background, Texture, Photoshop Structure style CC0 texture.
Source Darkmoon1968
Not even 1kb, but very stylish. Gray thin lines.
Source Struck Axiom
From a drawing in 'Studies for Stories', Jean Ingelow, 1864.
Source Firkin
A background pattern with wavy green vertical stripes. This one has green stripes on a white background. Download if you like it.
Source V. Hartikainen
The image depicts a seamless pattern of a snow crystal.I referred to a book called ”sekka-zusetsu” or "雪華図説" which means an illustrated explanation about snow crystals.This book was published in 1832 (天保3年) or Edo period.For more about "雪華図説",see here:dl.ndl.go.jp/info:ndljp/pid/2536975
Source Yamachem
Kaleidoscope Prismatic Abstract No Background
Source GDJ
A monochrome pattern from a tile that can be had by selecting the rectangle in Inkscaope and using shift+alt+i
Source Firkin
Just the symbols of the signs of the zodiac distributed in a chequer board-like pattern
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
This is so subtle you need to bring your magnifier!
Source Carlos Valdez
Super subtle indeed, a medium gray pattern with tiny dots in a grid.
Source Designova
Prismatic Hypnotic Pattern 2 No Background
Source GDJ
Dark, square, clean and tidy. What more can you ask for?
Source Jaromír Kavan
Remixed from a drawing in 'The Canadian horticulturist', 1892
Source Firkin