Not so subtle. These tileable wood patterns are very useful.
Source Elemis
A playful triangle pattern with different shades of gray.
Source Dimitrie Hoekstra
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
The image depicts a Japanese Edo pattern called "kanoko or 鹿の子" meaning "fawn" which has a fur with small white spots.
Source Yamachem
Continuing the geometric trend, here is one more.
Source Mike Warner
A seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin
This background pattern contains a seamless texture of bark. It's not very realistic, but I think it looks quite nice.
Source V. Hartikainen
Dare I call this a «flat pattern»? Probably not.
Source Dax Kieran
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin