Real snow that tiles, not easy. This is not perfect, but an attempt.
Source Atle Mo
A seamless pattern formed from a tile made from page ornament 22. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Abstract Background Design No Black
Source GDJ
Might not be super subtle, but quite original in its form.
Source Alex Smith
Imagine you zoomed in 1000X on some fabric. But then it turned out to be a skeleton!
Source Angelica
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
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
Abstract Tiled Background Extended 11
Source GDJ
An abstract texture of water. It's not perfect, but will do. You may download if you like it.
Source V. Hartikainen
Dare I call this a «flat pattern»? Probably not.
Source Dax Kieran
The image is a seamless pattern of a fishnet.
Source Yamachem
Number 2 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
A white version of the very popular linen pattern.
Source Ant Ekşiler
Inspired by a design found in 'Konstantinápolyi emlékeim', Miklos Chriszto, 1893.
Source Firkin
A seamless web background with texture of aged grid paper.
Source V. Hartikainen
Bigger is better, right? So here you have some large carbon fiber.
Source Factorio.us Collective
From a drawing in 'Studies for Stories', Jean Ingelow, 1864.
Source Firkin
Floral patterns might not be the hottest thing right now, but you never know when you need it!
Source Lauren
A large (588x375px) sand-colored pattern for your ever-growing collection. Shrink at will.
Source Alex Tapein
Light gray pattern with an almost wall tile-like appearance.
Source Markus Tinner
Here's a new paper-like background for free use on personal and commercial projects (this applies to all background patterns here).
Source V. Hartikainen
Pattern formed from simple shapes. Black version.
Source Firkin