Not strictly seamless in that opposite edges are not identical. But they do marry up to make an interesting pattern
Source Firkin
Prismatic Curved Diamond Pattern 4 No Background
Source GDJ
One more from Badhon, sharp horizontal lines making an embossed paper feeling.
Source Badhon Ebrahim
A seamless web background with texture of aged grid paper.
Source V. Hartikainen
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Love me some light mesh on a Monday. Sharp.
Source Wilmotte Bastien
Might not be super subtle, but quite original in its form.
Source Alex Smith
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Oh yes, it happened! A pattern in full color.
Source Atle Mo
Used in small doses, this could be a nice subtle pattern. Used on a large surface, it’s dirty!
Source Paul Reulat
Sort of like the Photoshop transparent background, but better!
Source Alex Parker
Geometric triangles seem to be quite hot these days.
Source Pixeden
Prismatic Hypnotic Pattern No Background
Source GDJ
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin
This is a seamless pattern of regular hexagon which has a honeycomb structure.
Source Yamachem
Dark, square, clean and tidy. What more can you ask for?
Source Jaromír Kavan
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
Pattern that came out of playing with the 'slinky' plug-in for Paint.net
Source Firkin
Prismatic Groovy Concentric Background 2
Source GDJ
This background pattern contains worn out colorful stripes as a texture.
Source V. Hartikainen