I skipped number 3, because it wasn’t all that great. Sorry.
Source Dima Shiper
Zero CC tileable cork floor, photographed and made by me. CC0
Source Sojan Janso
A new take on the black linen pattern. Softer this time.
Source Atle Mo
Feel free to download this "Dark Wood" background texture for your web site. The background tiles seamlessly!
Source V. Hartikainen
A seamless tessellation pattern. To get the tile this is formed from, select the pattern in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Floral Background No Black
Source GDJ
From a drawing in 'Az Osztrák-Magyar Monarchia irásban és képben', 1885.
Source Firkin
Some more diagonal lines and noise, because you know you want it.
Source Atle Mo
Looks like a technical drawing board: small squares forming a nice grid.
Source We Are Pixel8
Light square grid pattern, great for a “DIY projects” sort of website, maybe?
Source Rafael Almeida
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
A car pattern?! Can it be subtle? I say yes!
Source Radosław Rzepecki
Remixed from a drawing in 'Incidents on a Journey through Nubia to Darfoor', F. Ensor, 1891.
Source Firkin
Super detailed 16×16 tile that forms a beautiful pattern of straws.
Source Pavel
Sounds like something from World of Warcraft. Has to be good.
Source Tony Kinard