I skipped number 3, because it wasn’t all that great. Sorry.
Source Dima Shiper
Sounds like something from World of Warcraft. Has to be good.
Source Tony Kinard
A repeating background of beige paper with vintage look. Repeats to infinity, as usual.
Source V. Hartikainen
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
It’s okay to be square! A nice light gray pattern with random squares.
Source Waseem Dahman
This is a seamless pattern which is derived from a flower petal image.
Source Yamachem
This texture looks like old leather. It should look great as a background on web pages.
Source V. Hartikainen
Classy golf-pants pattern, or crossed stripes if you will.
Source Will Monson
Prismatic Abstract Background Design No Black
Source GDJ
A topographic map like this has actually been requested a few times, so here you go!
Source Sam Feyaerts
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
A seamless web texture of "green stone".
Source V. Hartikainen
Remixed from a drawing in 'Works. Popular edition', John Ruskin, 1886.
Source Firkin
Colour version of the original pattern inspired by the front cover of 'Old and New Paris', Henry Edwards, 1894.
Source Firkin
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
Got some felt in my mailbox today, so I scanned it for you to use.
Source Atle Mo
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A seamless stone-like background for blogs or any other type of websites.
Source V. Hartikainen
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
You could get a bit dizzy from this one, but it might come in handy.
Source Dertig Media
Lovely pattern with splattered vintage speckles.
Source David Pomfret
Looks like a technical drawing board: small squares forming a nice grid.
Source We Are Pixel8