The Steam Summer Sale 2016 has begun!

It will last until 04. July 2016.

The Lunar New Year Sale on Steam has begun and it will last until 12.02.2016!

The Steam Winter Sale 2015 has begun!

Here is a (currently incomplete because still updating) list of the current discounts for Linux games (from https://steamdb.info/sales/?displayOnly=all&category=999&cc=uk):

The Winter-Sale at GOG has begun!
The sale will last for 11 days, until December 13, 1:59 PM GMT / 2:59 PM CET / 5:59 AM PST / 8:59 AM EST.

After the first 48 hours, the games will be discounted in a 24 hours rythm, so take a look often!

This time you can get two games for free: Divine Divinity after spending $5, and Blackguards Special Edition after spending $50 or more.

The complete launch-text follows:

The so called "Steam Exploration Sale" has recently begun!
It lasts until 01.12.2015 and for the first time ever it has only lasting discounts (no more "Daily Deals").

These are all discounted games for Linux:

http://store.steampowered.com/search/?specials=1&os=linux

Since today is the official release of the Steam Machines, Valve has started the Steam Machines Launch Sale.
From A like Alien Isolation to X like XCOM: Enemy Unknown you'll find many discounted Linux-games.

Just a few moments ago GOG have announced it: the Big Fall Sale has begun.

It will last until November, 15th and promises discounts up to 90%. If you even manage to spent a total of $30 (or more) in this timeframe, you can get up to three games (incl. Banished) for free!

But read for yourself, here is the cite from their Website:

350+ daily deals and bundles up to -90%. Free games to unlock. Fuzzy squirrel on the front page.