Oh man I got so many great games to recommend. Let me try and make a selection.
The Last Door series Very atmospheric pixel point-and-click games.
K. O. L. M. A metroidvania where you're a robot recollecting your parts. Also has a
sequel where you keep all your upgrades from the first game, plus there's a second playable character that teams up with you. (Saying more would be spoilers but it's pretty neat.)
Boddy Ladder A game where you fight on an ever increasing pile of your enemies' corpses. Has some flaws but the concept is badass enough to get away with it.
no-one has to die Narrative-focused puzzle game. If there's one thing from this list you play, make it this one. It's probably one of my favorite games ever.
Fear Less Help Little Red Riding Hood(?) overcome her nightmares where she's being chased by Death in a forest and turn her into a fox and/or wolf slaying double-jumping badass.
Second Person Shooter Zato It's a second person shooter, what more do you need to know?
Rebuild Post zombie apocalypse city management. Has a 2 and 3 as well, but I like the first one good enough.
Edmus A pretty simple runner game, but you can see past lives of yourself and other players (and laugh at them as half of them die the first 20 seconds).
Canabalt Another runner, one of the early ones. Mostly known for having the most awesome non-existent plot. You'll see what I mean.
This Is The Only Level Except you'll need to beat it over and over again, each time with another game-changing rule applied. Has a sequel too! Both are great.
Death Dice Overdose There's giant dice falling from the sky and this is bad news. The greatest part of this game is the pill system; if you don't collect enough pills, you die of shock. If you collect a whole bunch of them, things become 'a little crazy'. Also has really pumpin' music.
The Company of Myself A puzzle game based around the life story of a hermit. Also has a prequel 'Fixation' which is essentially an entirely different game about the same characters.
Don't Look Back A platformed based on the story of Orpheus and Eurydice.
Achievement Unlocked By the creator of This Is The Only Level (and other cool stuff) this is somewhat similar except, well, I'm sure the title gives you a good idea of what you'll be doing.
I've got more where that came from so if there's a type of games you like in particular feel free to ask. I used to play a LOT of flash games.
Oh by the way
- Spoiler:
Booyeah!