Rare Giveaway

Assassin's Creed Rogue has only one giveaway: https://www.steamgifts.com/archive/search?q=Assassin%27s%20Creed%20-%20Rogue

Baldur's Gate II's last public giveaway was 9 months ago: https://www.steamgifts.com/archive/search?q=baldur%27s%20gate%20II

https://www.steamgifts.com/archive/search?q=hyper%20light%20drifter <--- Hyper Light Drifter (2 public GAs 2 month ago)
And already mentioned Salt and Sanctuary & Axiom Verge
I already own all this titles, but games are great and rare in GAs

Gun
Kingdom Rush Frontiers

Factorio is exactly $20.00
Zero public giveaway in last 2 months

Baldur's Gate: Siege of Dragonspear (Release Date: 31 Mar, 2016 - Given away two times as group giveaways).
I upvoted other game with +1 earlier (Salt and Sanctuary) so if one user can't suggest two, then take my vote off from this game

STASIS
It was given away in a public GA once in the last 2 months

So... here we go:
Rabi-Ribi, no public giveaways at all, https://www.steamgifts.com/archive/search?q=rabi-ribi
Time Tenshi, 1 public giveaway in the last 2 months, https://www.steamgifts.com/archive/search?q=time%20tenshi
Sakura Dungeon, 2 public giveaways in the last 2 months, https://www.steamgifts.com/archive/search?q=sakura%20dungeon

Wailing Heights: http://store.steampowered.com/app/443650/ - archive page
Released in April, 4 giveaways in total, none of them public.
The game is only 9.99, but there's the Deluxe Edition with juicy content that comes a bit pricier.

Battlezone 98 Redux. A hidden gem

• Brigador (2 giveaways) / Steam link
• Rodina (3 giveaways) / Steam link
• Dungeon Kingdom: Sign of the Moon (3 giveaways) / Steam link

only 1 giveaway for Black Closet http://steamcommunity.com/app/400580
only 2 giveaways for Pharaonic http://store.steampowered.com/app/386080 (this one is quite recent)
only 3 giveaways for Shardlight http://store.steampowered.com/app/336130
only 1 giveaway for Cardinal Quest 2 http://store.steampowered.com/app/378030

Reiner Knizia's The Confrontation appears to have never once before been given away on Steamgifts.

(Some additional options:)
Icebound: 1 giveaway: 1 group
Enigma: An illusion named family: 1 giveaway: 1 group
Doom & Destiny Advanced: 3 giveaways: 2 group, 1 public
Templar Battleforce: 6 giveaways: 4 group, 1 group+region-restricted, 1 high-level public.
I Shall Remain: 7 giveaways: 3 group, 4 high-level public.
Cursed Sight: 8 giveaways: 5 group, 1 invite-only, 1 region-restricted, 1 invite-only + region restricted
The Amber Throne: 9 giveaways: +1 it here

Amphora - http://store.steampowered.com/app/331510 (might not count since it`s at limit, with 5 giveaways...)

Firewatch - 20$ - 1 public, not region restricted, any level giveaways in last two month / 100 giveaways at all times - 11 rank in steamgifts wishlist
Ori and the Blind Forest: Definitive Edition - 20$ - 6 / 27 GAs - 14 rank
This Is the Police - 15$ - 2 / 25 GAs - 51 rank
The Flame in the Flood - 20$ - 0 / 37 GAs - 65 rank
Oxenfree - 20$ - 0 / 36 GAs - 73 rank
Armello - 15$ - 1 / 46 GAs - 134 rank
Don't Starve - 15$ - 2 / 1563 GAs -188 rank
Dead In Bermuda - 15$ - 0 /19 GAs - 216 rank
The Flame in the Flood - 20$ - 0 / 37 GAs - 65 rank
1979 Revolution: Black Friday - 12$ - 2 / 18 GAs - 188 rank
The Banner Saga 2 - 20$ - 0 / 33 GAs - 133 rank
Stories: The Path of Destinies - 15$ - 0 / 15 GAs - 84 rank
The Cave - 15$ - 2 / 378 GAs - 218 rank

Lots of great mentions so far.

I'll throw in Serpent in the Staglands, only given away 4 times so far and once in the past two months.

Bioshock Infinite season pass, cough... I dont think you need proof on that one

Last Days of Old Earth has never been given away. It's 23€ on Steam, but it's on sale on Bundle Stars for the next 3 days, for a bit less than 20€ : https://www.bundlestars.com/en/game/last-days-of-old-earth

House of the Dying Sun had only 1 GA.

A Little Lily Princess no Public GA in last 2 Months.

This thread is adding a bunch of games to my wishlist -.-.

Kona
The Town of Light

And listed previously:
1979 Revolution: Black Friday

Monkey Island 2: Lechuck's Revenge Special Edition
https://www.steamgifts.com/archive/search?q=lechuck
or the special edition bundle
https://www.steamgifts.com/archive/search?q=monkey%20island%3A%20special%20edition%20bundle
I think is also less than $20

Descent Underground. Would really love to have it. And thanks for the offer. That's very sweet of you.

Woops. Misread. Aquaria. It's a great game and on my wishlist. Costs $9.99 on Steam