This seamless background image should look nice on websites. It has a dark blue gray texture with vertical stripes, it tiles seamlessly and, like all of the background images here, it's free. So, if you like it, take it!
Source V. Hartikainen
Zero CC tileable hard cover green book, scanned and made by me. CC0
Source Sojan Janso
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857. The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Love me some light mesh on a Monday. Sharp.
Source Wilmotte Bastien
This one takes you back to math class. Classic mathematic board underlay.
Source Josh Green
Seamless pattern formed from a tile that can be extracted by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A comeback for you: the popular Escheresque, now in black.
Source Patten
From a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin