I'll play! Thanks, Victor, for getting this started.
Caveat: my IF involvement has been minimal for the past several years, so this is going to be heavily weighted toward older games. (In particular, I suspect, from what I've read, that Blue Lacuna, Chancellor, Make it Good, Everybody Dies, Cryptozookeeper, Deadline Enchanter, Distress, King of Shreds and Patches, Alabaster, First Things First, and Floatpoint would at least be strong candidates for this list, had I played them. And I have no good excuse for never having finished Bad Machine.) Hopefully that will be balanced out by newbies who never got around to playing older stuff.
My 20, in roughly this order:
1. Spider and Web. Not much to add to what's been said above, and elsewhere. The single best marriage of puzzle and story to date, in my view. and while the central device has been used in static fiction, its effect is magnified by interactivity.
2. Trinity. Strong puzzles, engaging story, and one particular moment that (arguably) introduced the idea of the player's complicity in the plot.
3. Varicella. Viciously difficult, but well worth the many playthroughs it takes to finish. Perhaps the most fitting ending in all of IF.
4. Spellbreaker. Evocative mood, difficult-but-fair puzzles.
5. Anchorhead. Mood builds gradually, and the writing is appropriately restrained; the puzzles are designed in a way that, for the most part, draws out the plot but doesn't bring it to a halt. (The endgame, with some tight timing required, is an exception, but not egregiously so.) Well-designed storytelling that can be enjoyed even by those who don't care for Lovecraft.
6. So Far. More a mood piece than a narrative, but the mood is effectively done, and the puzzles, while sometimes cruel, are worth noodling over.
7. Zork III. The best puzzles of the trilogy (setting aside the timed event that makes the game unforeseeably unwinnable), the most consistently done atmosphere, and a sly subversion of the treasure hunt.
8. Worlds Apart. My memories of this one have grown slightly fuzzy, I confess, but I do remember extraordinarily deep worldbuilding, several well-drawn characters, and puzzles that serve rather than impede the plot.
9. Slouching Toward Bedlam. Not sure moral choice in IF has been done better.
10. Metamorphoses. Notable for the depth of its implementation--in particular, there are devices that can transmute objects into different substances, and the game does a remarkable job of accommodating all the possibilities--and for the indirect way the story is told.
11. Losing Your Grip. It may not be the only IF game that centers on exploration of the protagonist's own mind, but it's the only one I know of that's done it well. Not perfectly--I've never managed to make sense of some of it--but on the whole it rewards close analysis.
12. Augmented Fourth. Somewhat underdiscussed on the IF scene, this one deserves to be better-known; it's a witty sendup of/homage to the fantasy genre with not-too-hard puzzles and some genuinely hilarious prose. The opening scene, where the narrator is being tossed into a pit and mocked by some not-too-bright guards, is particularly good.
13. Lost Pig. The every-response-is-implemented game par excellence, and many, many laugh-out-loud moments.
14. Sunset Over Savannah. Another mood piece, beautifully written, with difficult but well-hinted puzzles.
15. Shadow in the Cathedral. Linear, but takes advantages of the strength of linearity--a strong sense that the puzzle-solving is driving the plot--without making the player feel railroaded. Well-told story, with some very good puzzles and some nice tense moments.
16. Wishbringer. The first, to my knowledge, and the best IF game to deploy the nightmare-version-of-familiar-landscape approach. Lots of multiple-solution puzzles at a time when that wasn't common. The puzzles are kid-oriented, but there's plenty of sly humor.
17. Jigsaw. Some of the puzzles are, in my view, flat-out unfair. But many are just right, and the scope and thoroughness of the thing keeps this among my faves.
18. Small World. Another mostly forgotten game, this one from the 1996 competition. Clever, tricky-but-logical puzzles, and a very funny NPC.
19. Shade. Some touchy event triggers, but still the best mess-with-your-head IF I can think of.
20. Infidel. Lots of clever mechanical puzzles, and an ending that left me slackjawed.
Honorable mentions: Savoir Faire, Christminster, Delusions, Enchanter, City of Secrets, All Things Devours, Not Just an Ordinary Ballerina, Mulldoon Legacy, Dreamhold, Curses, A Mind Forever Voyaging, Galatea, Hunter, in Darkness, Change in the Weather, Suspended, Bronze, The Gostak, Ad Verbum, Moonlit Tower, Fear, Till Death Makes a Monk-Fish Out of Me!, Babel, Zero Sum Game, Janitor, Lurking Horror, Rameses, Rematch, Little Blue Men, Plundered Hearts, For a Change, A Day for Soft Food, A Bear's Night Out, Goose, Egg, Badger, Blighted Isle, Kissing the Buddha's Feet, Lydia's Heart, Violet, Maiden of the Moonlight, Ballyhoo, Djinni Chronicles, Inevitable, LASH, Pytho's Mask, The Weapon, Insight, All Hope Abandon, The Edifice, Scavenger, Heroes, Child's Play
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Victor asked for a list of favorites, but I wonder if there's value in considering what IF we think is objectively the "best," rather than our subjective faves. My view, for what it's worth, is that IF is usually "best" when it most successfully merges story and puzzle, as this medium can do that better than any other. I.e., puzzles that are fully motivated by the plot and organic to the story, not set pieces or "say, here's a locked door, I will stop at nothing to unlock it" types--and advance the narrative rather than putting it on hold. Vividly drawn characters and settings are important too, but a novel can, I think, convey those just as well as IF can. (Admittedly, interactivity makes a difference in how one *experiences* characters and settings, but I don't think we're at the point where IF can clearly depict either *better* than static fiction can.)
Of course, the quality of the story matters too; a flawless game about going to the mailbox wouldn't make my list. Telling a story that matters is important--and the way it's told is just as important. The other way this medium improves on static fiction is finding ways to make the player's role in driving the story give it additional power--complicity, in other words--and games that effectively use IF's unique storytelling force should also be considered among the "best." Relatively few games make much of this, but those that do are, in my view, particularly noteworthy.
For myself, I'd put most of my 20 faves above among the "best" in this sense as well, but not all. As fond as I am of Spellbreaker, for example, I can't dispute that the plot is mostly absent, and it doesn't motivate the puzzle-solving except in the most general sense. Trinity is better in that regard, but still has long stretches where there's no obvious connection between the puzzle-solving and your ultimate goal. Smaller, more focused games like Child's Play, Delusions, Djinni Chronicles, and Change in the Weather integrate the puzzles and story much more tightly. And while Trinity has a "complicity" moment, it's just one moment; other games like Heroes and Bad Machine have done more with that idea.
(Sadly, I lack the time to replay all of my faves to reassess how successful they are on these metrics; I remember what I enjoyed about them, but not necessarily how well they motivate their puzzle-solving, say.)
Or am I just overthinking this?