xkcd - Updates M/W/F - Stick figure comic. Nerdy as hell, but you're on Neocities, so I figure you are too. Highly recommend.
SMBC - Updates weekdays - Fun comic, lots of single-panel jokes. Only slightly less nerdy than xkcd.
Homestuck/MSPA - No longer updates (completed) - Oh God, why is this on the list? Don't check this one out unless you think you're ready. Reading from the beginning *highly* recommended.
Questionable Content - Updates weekdays - Comedic slice-of-life. Questionable quality, not Questionable the other way. Honestly warrants a warning more than Homestuck does. Reading from the beginning recommended.
Awful Hospital - Updates whenever - High-concept, narrative-driven, body horror interactive fiction. I very much recommend this one to anyone who can stomach it.
Octopus Pie - No longer updates (completed) - Jokey slice-of-life that becomes surprisingly emotional by the end. Scott Pilgrim-esque.
Nothing Doing - Updates whenever - Actually funny office comedy. Only 60 strips as of writing, but they're good stuff!
Slashfic - Updates whenever - AW FUCK I FORGOT TO MENTION SLASHFIC UNTIL NOW. GO READ IT
Dolmistaska - Updates whenever - Urban fantasy... sci-fi... absurdist thing? The best way to get the vibe across succinctly would be "anarchist."
UNDERTALE - $9.99 on Steam, up to $19.99 elsewhere - It's 2025. You know UNDERTALE. On the 1% chance you haven't actually played UNDERTALE, or been spoiled on it, go do that.
Ad Verbum - Free in browser! - Wordplay-heavy text adventure game. Short but sweet. Every puzzle will either make you feel really clever for figuring it out quickly or really stupid for taking so long.
Blackbox - Free with in-app purchases, no ads, iOS-only - Tricky, transreal, abstract puzzle game. Really plays with out-of-the-box puzzle solving. As above, every puzzle will either make you feel really clever or really stupid.
Cryptmaster - $24.99 - Fun text-based RPG. Lots of good riddles, puzzles, and rife with secrets.
Slay the Princess: The Pristine Cut - $17.99, available everywhere - *Very*, *very* good horror visual novel, and I say this as someone who is neither a big horror person nor visual novel person. Incredible story, beautiful art and music. The type of game that you should play with as few spoilers as possible.