Most game links go to the relevant entry of Baf's Guide to the Interactive Fiction Archive.
Savoir Faire by Emily Short. In all likelihood my favouritest IF piece. At its heart it's a old-skool puzzler, though almost all the puzzles are strikingly innovative. It's also beautifully written, evocative and pretty damn big. Beautiful.
Lock & Key by Adam Cadre. This is only IF by default, really, but it's also very funny, devilishly difficult and deeply satisfying to complete. Schlock-fantasy, with all the trimmings.
Fallacy of Dawn by Robb Sherwin. Think Blade Runner meets Red Dwarf in order to eat pizza and play videogames. One of the funniest games about, although it's somewhat buggy in parts. Earns extra points for thoroughly appropriate graphics use.
Photopia by Adam Cadre. Emotionally powerful, though much-criticised for its heavily linear structure and lack of interactivity; ironic given its opening lines. A must-play, however.
Metamorphoses by Emily Short. The most overtly Neoplatonic of Short's games; a shameless puzzlefest as dreamt up by a Renaissance occultist.
Galatea by Emily Short. A showcase of NPC conversation; a bristling phalanx of multiple endings; a joy to play.
Anchorhead by Michael Gentry. Lovecraftian horror; a superb example of how wandering about solving puzzles for hours and hours needn't be detrimental to atmosphere and plot.
Time Bastard by Matt Fendalaheen. It's only a transcript of a non-existent game, but it'd be one hell of a game if it had ever been implemented. Psychopathic gross-out injokes with Cthulhu on the side? Lovely.
Spider & Web by Andrew Plotkin. Dark; high-tech espionage on a Cold War-like backdrop. Insanely difficult, with a marvellous narrative structure.
Shrapnel by Adam Cadre. Short, chaotic and with a whole lot of visceral impact.
City of Secrets by Emily Short. Massive, NPC-heavy, richly detailed, thematically rich. Sprawling, which may or may not be an advantage; high-quality writing throughout, however.
Moonlit Tower by Yoon Ha Lee. A beautifully delicate piece, if somewhat directionless and vague; the agglomeration of Far Eastern mythologies is ever so slightly grating, and the puzzles get a little abtruse at times, but overall I love this.
Shadows on the Mirror by Chrysoula Tzavelas. Conversation-driven; moody and atmospheric, although I feel it becomes a little overblown towards the end.
Bad Machine by Dan Shiovitz. An impressive feat of implementation if nothing else; as with other strikingly unique games, it demands a radically different style of approach from the player. Macabre, complex, and difficult.
Best of Three by Emily Short. Conversation-heavy, more mundane and down-to-earth and in some ways more personal than the rest of Short's stuff. A lot of fun to explore.
Varicella by Adam Cadre. Machiavellian intrigue set against Italian city-states with modern fittings. Dark and funny, the two things Adam does best.
Slouching Towards Bedlam by Daniel Ravipinto and Star Foster. Dark steampunk-with-cabbala stuff. A little slow to get off the ground, but otherwise excellent.
Vespers by Jason Devlin. Plague, snow, wolves, starvation, sin, fire, and the God turning his face away; the medieval period, in other words. If you can take the bleakness, this is a joy to play.
Best of Three by Emily Short. Conversation-heavy, more mundane and down-to-earth and in some ways more personal than the rest of Short's stuff. A lot of fun to explore.
Varicella by Adam Cadre. Machiavellian intrigue set against Italian city-states with modern fittings. Dark and funny, the two things Adam does best.

Other recommended-IF sites:
Baf's Guide to the Interactive Fiction Archive is an essential resource.
Chrysoula Tzavelas' IF Ratings site is a public voting system that offers a list of highest-rated games. (The more people who use it, the more powerful it becomes, so if you're feeling public-spirited get an account and rate games as you play 'em). The highest-rated games are generally worth playing, if only so you can have an opinion of 'em.
Emily Short's site has a fairly comprehensive listing, intended to list games which employ interesting techniques rather than a straight Best Of.
Suzanne Britton's recommendations are definitely worth a look, although the page hasn't been updated for a while and hence won't contain new releases.

Why Isn't My Stupid Favourite Game Here? Because either I haven't got around to playing it yet, or I didn't like it. Go on, whine to me. I dare ya.