I skipped number 3, because it wasn’t all that great. Sorry.
Source Dima Shiper
Prismatic Snowflakes Pattern 3 No Background
Source GDJ
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Some more diagonal lines and noise, because you know you want it.
Source Atle Mo
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
Medium gray fabric pattern with 45-degree lines going across.
Source Atle Mo
A seamless pattern formed from a square tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-i
Source Firkin
A seamless pattern formed from a square tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-I. A version of the original with random colors.
Source Firkin
This tiled background comes in red and consists of tiles that look like gemstones. It is more for blogs or social profiles, I think.
Source V. Hartikainen
Classic vertical lines, in all its subtlety.
Source Cody L
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Prismatic Geometric Pattern Background No Black
Source GDJ
Remixed from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Light square grid pattern, great for a “DIY projects” sort of website, maybe?
Source Rafael Almeida
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Some dark 45 degree angles creating a nice pattern. Huge.
Source Dark Sharp Edges
A background formed from an image of an old tile on the New York Metropolitan Museum of Art website. To get the base tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
From a drawing in 'Handbook of the excursions proposed to be made by the Lincoln Diocesan Architectural Society, on the 27th and 28th of May, 1857', Edward Trollope, 1857.
Source Firkin
One of the few full-color patterns here, but this one was just too good to pass up.
Source Alexey Usoltsev
The act or state of corrugating or of being corrugated, a wrinkle; fold; furrow; ridge.
Source Anna Litvinuk
Here's an yet another seamless note paper texture for use as a background on websites.
Source V. Hartikainen
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight