A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
There are many carbon patterns, but this one is tiny.
Source Designova
A seamlessly repeating background pattern of wood. The image is procedurally generated, and, I think, it's turned out quite well.
Source V. Hartikainen
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Background pattern originally a PNG drawn in Paint.net
Source Firkin
Adapted from an image that was uploaded to Pixabay by Anerma.
Source Firkin
Here's a quite bright pink background pattern for use on websites. It doesn't look like a real fur, but it definitely resembles one.
Source V. Hartikainen
Prismatic Geometric Tessellation Pattern 4 No Background
Source GDJ
A light gray wall or floor (you decide) of concrete.
Source Atle Mo
Just like your old suit, all striped and smooth.
Source Alex Berkowitz
A seamless pattern the starting point for which was a 'colour modulo' texture in Paint.net.
Source Firkin
Prismatic Snowflakes Pattern No Background
Source GDJ