So, tallying some of the responses so far, these seem to be the ones most considered essential for each edition:
0E: Greyhawk and Eldritch Wizardry. The other two supplements important but less so.
Moldvay: Expert Rulebook (of course)
BECMI: Expert and Companion Rules, less so Master Rules. Creature Catalog(ue) is also key.
1E: UA is a bit controversial but mostly considered essential. Fiend Folio and MM II. The Dungeoneer's Survival Guide is also important.
2E: The Complete Fighter's Handbook seems like a must. Followed by Complete Thief, and then Priest and Wizard. Of Player's Option books, Combat & Tactics and High-Level Campaigns are seen as important, but the other two not so much. Other important rulebooks: Complete Psionics, Tome of Magic, Arms & Equipment Guide. Aurora's Whole Realms Catalog, while setting-specific, is also well-regarded.
3.0: All five class books are considered the most important, followed by the Epic Level Handbook, Savage Species, and the Arms and Equipment Guide.
3.5: Book of Nine Swords got strong support (though also a little controversal). Complete Divine appears to be the best-regarded of the Complete series, followed by Fighter, Mage, and Arcane. PHB II, DMG II, and UA are important.
4E: MM 3 is the most popular of the core rules expansions, followed by PHB 2 and MM 2. Martial Power seems to be the best-regarded of the Power books.
5E: Xanathar's is by far the most essential, though MOTM is also up there, followed by Tasha's.
Interesting to see how some of you thought of certain setting-specific products as essential...
0E: Greyhawk and Eldritch Wizardry. The other two supplements important but less so.
Moldvay: Expert Rulebook (of course)
BECMI: Expert and Companion Rules, less so Master Rules. Creature Catalog(ue) is also key.
1E: UA is a bit controversial but mostly considered essential. Fiend Folio and MM II. The Dungeoneer's Survival Guide is also important.
2E: The Complete Fighter's Handbook seems like a must. Followed by Complete Thief, and then Priest and Wizard. Of Player's Option books, Combat & Tactics and High-Level Campaigns are seen as important, but the other two not so much. Other important rulebooks: Complete Psionics, Tome of Magic, Arms & Equipment Guide. Aurora's Whole Realms Catalog, while setting-specific, is also well-regarded.
3.0: All five class books are considered the most important, followed by the Epic Level Handbook, Savage Species, and the Arms and Equipment Guide.
3.5: Book of Nine Swords got strong support (though also a little controversal). Complete Divine appears to be the best-regarded of the Complete series, followed by Fighter, Mage, and Arcane. PHB II, DMG II, and UA are important.
4E: MM 3 is the most popular of the core rules expansions, followed by PHB 2 and MM 2. Martial Power seems to be the best-regarded of the Power books.
5E: Xanathar's is by far the most essential, though MOTM is also up there, followed by Tasha's.
Interesting to see how some of you thought of certain setting-specific products as essential...