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 pattern with a unit cell drawn as a bitmap in Paint.net and vectorized in Vector Magic.
Source Firkin
Here's an yet another background for websites, with a seamless texture of wood planks this time.
Source V. Hartikainen
A light gray wall or floor (you decide) of concrete.
Source Atle Mo
Crossing lines with a subtle emboss effect on a dark background.
Source Stefan Aleksić
Tweed is back in style – you heard it here first. Also, the @2X version here is great!
Source Simon Leo
This one is rather fun and playful. The 2X could be used at 1X too!
Source Welsley
The image depicts meshed silhouettes of various things.The original image is an OCAL clipart called "Enter FOSSASIA 2016 #IoT T-shirt Design Contest" uploaded by "openclipart".Thanks.
Source Yamachem
Number 2 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
This background pattern looks like bamboo to me. Feel free to download it for your website (for your blog perhaps?).
Source V. Hartikainen
Derived from elements found in a floral ornament drawing on Pixabay.
Source Firkin
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
Number 3 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
The rectangular tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Crossing lines with a subtle emboss effect on a dark background.
Source Stefan Aleksić
It’s a hole, in a pattern. On your website. Dig it!
Source Josh Green
Adapted from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
A seamless pattern formed from background pattern 102
Source Firkin
Prismatic Curved Diamond Pattern 5 No Background
Source GDJ
This pack of filters can help you adding a blocky overlay to objects. May come handy at drawing blocks of stone.
Source Lazur URH
Like the name suggests, this background image consists of a pattern of dark bricks. It may be an option for you, if you are looking for something that looks like a brick wall for use as a background on web pages. It's not a masterpiece, but looks pretty nice when is tiled.
Source V. Hartikainen