Not strictly seamless in that opposite edges are not identical. But they do marry up to make an interesting pattern
Source Firkin
Dark, crisp and subtle. Tiny black lines on top of some noise.
Source Wilmotte Bastien
Prismatic Geometric Tessellation Pattern No Background
Source GDJ
A seamless pattern based on a square tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
Dead simple but beautiful horizontal line pattern.
Source Fabian Schultz
Floral patterns might not be the hottest thing right now, but you never know when you need it!
Source Lauren
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
You know you love wood patterns, so here’s one more.
Source Richard Tabor
Green Web Background, Seamless tile.
Source V. Hartikainen
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
Zero CC tileable hard cover green book, scanned and made by me. CC0
Source Sojan Janso