Practice Run by Floraverse
A thoroughly enjoyable, short, but highly replayable visual novel that puts you—you being a hyperactive bunny child named Kid Neon—in a ridiculous situation with your personal robot. You've convinced the 'bot to pretend to be your date, so you can get in a bit of practice, and it's the fastidious machine's frequent interjections and exasperation at the amusing dialogue options that make this a game you should download sharpish. Bonus points for the great Phoenix Wright joke.
Doctor Robot by Quantum Sheep
In a similar vein, Quantum Sheep's Doctor Robot puts you inside a short, strange scene that you'll want to replay again and again (and again). In this wee browser game, you've come to a big mechanical doctor to get some help for what's ailing ya, although their bedside manner is questionable, to say the least. Sometimes it's just unhelpful, other times it's downright rude or nonsensical. The same goes for the dialogue of the nurse in the waiting room, and the frog-like person who's also waiting to be seen. Not every playthrough makes sense—I'm presuming there's some random dialogue generation going on behind the scenes—but enough changed in enough interesting ways to keep me coming back for a handful of doctor visits. (Via Warp Door)
Under the Bed by Khamelot
In this clever horror adventure, you play as a lad roaming his pitch-black house in the middle of the night. It is, of course, chock-full of monsters, but if you close your eyes by pausing the game with 'P', the boy will imagine a brightly lit scene with no 'orrible things in. Because kid logic, I suppose, this action makes the monsters eventually disappear, and makes for an engaging sidescrolling adventure where you'll have to rely on your memory to succeed.
Love is Moving by Jared Johnson
I wasn't sure what this was to start with, but Love is Moving soon revealed itself to be an admirably earnest, sweet, and insightful rumination on all things love. It's a sort of art installation that you explore by moving a little heart around, interacting with each strange scene in a variety of interesting ways. Completed scenes unlock vignettes dealing with a particular facet of being in love. When you've finished each, an icon representing that facet will begin to follow your heart around, your little loved-up avatar trailing the weight of life experience behind them.
Devil's Tuning Fork by Kevin Geisler
A smart and spooky puzzle game that's a little bit Portal, a little bit Scanner Sombre. Trapped in some kind of coma world that is frighteningly devoid of light, you have to rely on a magical tuning fork that allows you to pulse out echo-location-style noises—sounds that will briefly illuminate your surroundings. Holding the right mouse button sends out a constant low echo that lets you see the vague shape of the world, while a charged left click shoots out a bolt of sound that can be used to activate switches. As you gather all of the toys and complete each dim level, you hear the convincingly frightened voices of trapped children, who appear to be lost in the same maze as you. That's surely all the motivation you'll need to see this dark puzzle game through to its conclusion.