From a drawing in 'Picturesque New Guinea', J Lindt, 1887.
Source Firkin
Geometric triangles seem to be quite hot these days.
Source Pixeden
8 by 8 pixels, and just what the title says.
Source pixilated
An abstract texture of water. It's not perfect, but will do. You may download if you like it.
Source V. Hartikainen
Not sure if this is related to the Nami you get in Google image search, but hey, it’s nice!
Source Dertig Media
One of the few full-color patterns here, but this one was just too good to pass up.
Source Alexey Usoltsev
There are quite a few grid patterns, but this one is a super tiny grid with some dust for good measure.
Source Dominik Kiss
The classic notebook paper with horizontal stripes.
Source Are Sundnes
A seamlessly repeating background pattern of wood. The image is procedurally generated, and, I think, it's turned out quite well.
Source V. Hartikainen
A seamless background texture of old cardboard.
Source V. Hartikainen
Just to prove my point, here is a slightly modified dark version.
Source Atle Mo
Remixed from a drawing in 'Analecta Eboracensia', Thomas Widdrington, 1897.
Source Firkin
I have no idea what J Boo means by this name, but hey – it’s hot.
Source j Boo
Abstract Tiled Background Extended 6
Source GDJ
A colourful background drawn originally in paint.net and vectorised in Vector Magic.
Source Firkin
Not so subtle. These tileable wood patterns are very useful.
Source Elemis
This is the remix of "Tileable Wave Pattern 2" uploaded by "Arvin61r58".Thanks.I added a wire-mesh fence seamless pattern as a lower layer.
Source Yamachem
Can never have too many knitting patterns, especially as nice as this.
Source Victoria Spahn
A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
You know you can’t get enough of these linen-fabric-y patterns.
Source James Basoo
This is the remix of "Strawberry Pattern Background" uploaded by "GDJ". Thanks. I realigned strawberries so as to get seamless and changed the BG color.
Source Yamachem
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i.
Source Firkin