Any good games that are 1-2GB?

Rust or Starbound! :)

Minecraft

Brother : A tale of two sons. but it requires a Controller.

If you're talking about pc then i suggest, Mark of the ninja 2.1 gigs though, i just grabbed a copy this morning and it's an amazing game! :)

Can't really help out with handheld apps, not much of an ios or android player.

reus

recently downloaded and tried, looks promising if you like that genre

Edit: Reread your topic. Oops. Here's a different list.

Ys Origin - 1911 mb
Ys: The Oath in Felghana - 1273 mb
Dust: An Elysian Tail - 1531 mb

Fez!

Binding of Isaac, Super Meat Boy, Trine, Awesomenauts, Any Mount and Blade game, Starbound, Surgeon Simulator 2013, Little Inferno, Thomas was Alone, The Stanley Parable, Torchlight II and many more! Maybe I should have looked at your games list.

Age of Empires 2

Savant - Ascent is a game that I recently played. I believe it's only ~60mb. The story mode itself you can beat in 10 minutes, but the other game modes and trying to 100% everything makes it worth a couple more hours or so. Also, the game is still being updated, so new content might come in.

From my library:
AoE II HD: 1554 without DLC -
Amnesia: The Dark Descent: 2358 mb -
Nail'd: 2217 mb -
Prince of Persia: Sands of Time: 1420 mb -
Prince of Persia: The Two Thrones: 1469 mb -
Risen: 2390 mb -
Shank: 1841 mb -
Shank 2: 1571 mb -
Trials Evolution: Gold Edition: 2885 mb -
Zeno Clash 2: 2843 mb

Deus ex original ~700mb
And System shock 2
And Half life 1

I can only think of good games that are less than 1 gig or more than one gig. At least half of my favorite games are under 1. Nothing in your range though.

FTL is much, much smaller than 1GB, and I'd say it's pretty damned good. :-)

State of Decay is pretty good but if you like old games then I recommend Deus Ex or System Shock 2.

Garry's Mod.

Dwaaaaaaaaaarf Fortreeessssssss

Ok if it has to be steam, try dominions 4.

Terraria, I think it was close to 50MB :)

Limbo.

Papers, please. The smallest game I played in awhile. But very interesting. Less than 40mb

Try older games .... like warcraft 3 or diablo 2 :D

Recettear: And Item Shop's Tale is a really fun and quirky little dungeon crawler, and it clocks in at 615 MB installed.

New games or older games? There's plenty of games on GOG and Steam that are 2GB or less: Arcanum, Planescape: Torment, Baldur's Gate, Baldur's Gate 2, Icewind Dale, Icewind Dale 2, the original Deus Ex (also on Steam but GOG gives you the real GOTY with soundtrack), and a ton more.

On Steam you can still get the Fallout Collection. I'm not sure if you can install the games separately on Steam, I have them on GOG and Fallout and Fallout 2 are both ~500MB while Tactics is 1.5GB.

Newer games I play that are ~2GB: Kerbal Space Program (I can't recommend this game enough), Don't Starve, Dungeons of Dredmore, Euro Truck Simulator 2 (surprisingly good game), FTL, Legend of Grimrock, Rogue Legacy, Sir You are Being Hunted, Space Pirates and Zombies, Stealth Bastard Deluxe,

Hearthstone 2.5 GB
Bastion 900 MB
FTL ~250 MB
To The Moon 100 MB
Bit Trip Runner 60 MB
Terraria 50 MB
Hack, Slash, Loot 9 MB