SweetShark said:
Out of those, I've played:
Don't Look Back
Judith
Today I Die
Dys4ia
I Remember the Rain
No-one Has to Die
Stupidella
Super Press Space To Win Adventure 2000
Thomas Was Alone
Personal Trip To The Moon
The Stanley Parable (that's not really unknown any more

)
Alpaca Run
Horse Master: The Game of Horse Mastery (I really, really like this one)
That's a fair amount, I think I deserve a pretentious hat

anyways, this is my list:
Interactive Fiction in which you are a Lizard [http://www.glorioustrainwrecks.com/node/2559] (seriously one of my favourite games of all time)
Frog Fractions [http://twinbeard.com/frog-fractions] (trust me)
Candy Box [http://candies.aniwey.net/] (this has a sequel, and I'm sorry for draining another few days of your life by mentioning that)
Bubsy 3D: Bubsy Visits the James Turrell Retrospective [http://bubsy3d.com/]
SUPERHOT [http://superhotgame.com/]
A Brief History of Cambodia [http://www.gametrekking.com/the-games/cambodia/a-brief-history-of-cambodia/play-now]
Test Subject Infinity [http://www.lockeddoorpuzzle.com/site/works/tsi]
A Salty Lass [http://www.escapistmagazine.com/content/indie-speed-run/?game=573]
Socrates Jones: Pro Philosopher [http://www.kongregate.com/games/ChiefWakamakamu/socrates-jones-pro-philosopher]
Omnidirectional Chaos [http://mattarod.com/chaosjam2x.html] (I beat this)
Pan Man [http://www.newgrounds.com/portal/view/622566]
Experiment 12 [http://distractionware.com/blog/2013/07/experiment-12/]
Naya's Quest [http://distractionware.com/blog/2013/09/nayas-quest/]
My First Kiss EXP [https://twitter.com/auntiepixelante/status/304478860429389825]
3 Blind Mice: A Remediation Game for Improper Children [http://seeminglypointless.com/mice/]
Crawl, Worm, Crawl! [http://polclarissou.com/CrawlWormCrawl/]
Is This A Game? [https://dl.dropboxusercontent.com/u/20534082/IsThisAGame.html]
Where the fuck is Richard? [http://gamejolt.com/games/other/where-the-fuck-is-richard/14877/]
You Have To Win The Game [http://www.piratehearts.com/blog/games/you-have-to-win-the-game/]
ASCIIvania [http://www.freeindiegam.es/2012/07/asciivania-gharding3/]
Cat Poke [http://jajitsu.com/games-html/cat-poke]
Cat Planet [http://www.ludumdare.com/compo/ludum-dare-16/?action=preview&uid=1081]
Pretentious Game [http://www.ludumdare.com/compo/ludum-dare-23/?action=preview&uid=12926]
陆霈的梦想 [http://sandbox.yoyogames.com/games/184009-%E9%99%86%E9%9C%88%E7%9A%84%E6%A2%A6%E6%83%B3]
Fox aliens from space invade a planet within space [http://sandbox.yoyogames.com/games/196253-fox-aliens-from-space-invade-a-planet-within-space#]
Socially Awkward Conversationalist [http://www.glorioustrainwrecks.com/node/2420]
Game Title [http://www.glorioustrainwrecks.com/node/2258]
Hero's Adventure [http://distractionware.com/blog/2011/08/heros-adventure/]
...aaand I've just realised like 2 people will play any of those games I just spent well over an hour listing

Seriously, if you're reading this and you just skipped through it, just click on one of them at least. You might not regret it
If anyone's interested in other games like the ones listed above (mine and Shark's), check out freeindiegam.es [http://www.freeindiegam.es/] - there's a lot of weird experimental stuff on there which is very hit-and-miss, but it's worth a look. It's also updated every day or two, so keep a bookmark.
Also, how do I get ahold of Train [http://www.listal.com/game/train-3ds-virtual-console]? I played one of their other games, The Light [http://www.freeindiegam.es/2013/08/the-light-sergey-noskov/], and couldn't find it. Thanks!