One of the few full-color patterns here, but this one was just too good to pass up.
Source Alexey Usoltsev
This is sort of fresh, but still feels a bit old school.
Source Martuchox
Here's a camo print with more tan and less green, such as might be used in a desert scenario. This is tileable, so it can be used as a wallpaper or background.
Source Eady
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
Continuing the geometric trend, here is one more.
Source Mike Warner
Prismatic Groovy Concentric Background 3
Source GDJ
This background pattern contains a texture of yellow wood planks. I think it looks quite original.
Source V. Hartikainen
ZeroCC tileable mossy (lichen) stone texture, edited from pixabay. CC0
Source Sojan Janso
I scanned a paper coffee cup. You know, in case you need it.
Source Atle Mo
From a drawing in 'Les Chroniqueurs de l'Histoire de France depuis les origines jusqu'au XVIe siècle', Henriette Witt, 1884.
Source Firkin
An interesting dark spotted pattern at an angle.
Source Hendrik Lammers
A seamless chequerboard pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i. Alternative colour scheme.
Source Firkin
You know I love paper patterns. Here is one from Stephen. Say thank you!
Source Stephen Gilbert
Prismatic Abstract Line Art Pattern Background 2
Source GDJ
This one resembles a black concrete wall when is tiled. It should look great, at least with dark website themes.
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin