Adventurer Conqueror King (either edition) - This is B/X with a bunch of tacked on crap dreamed up by someone with the soul of an accountant. I would hazard a guess and say everyone who plays this system is just playing B/X and ignoring all the busywork that's built in to the game and pretending it's a great thing. They would have just as good or a better time with just B/X. Which means they wasted their money as Basic Fantasy is free.
Basic Fantasy RPG (Iron Falcon) - This is the only true evolution of B/X that I've found (as in, an OSR of B/X that is just like B/X but better). As B/X is one of the two editions that are the bread and butter of the OSR, and the other edition (AD&D) is firmly in a secondary slot, That makes this game the quintessential OSR game. Look no further for all your B/X needs, meaning 80% of the OSR's supplemental material is intended for this game.
Castles & Crusades - See here. Rewrite of D&D3E to act like both B/X and expand it's baseline out to include AD&D1E. Intentionally nostalgic, existed before OSR and with the philosophy of people legit playing in 1983, when edition versions didn't really mean much and you stapled whatever from B/X and AD&D together, eyeballing balance. It's good right up until you include The Siege Engine, a wacky system that double-values ability scores (a lot like Dragonlance SAGA), where a "prime" stat of 3 is functionally as good as a non-prime stat at 18. While that's nonsense, it also marries scores to class ability further than either of the editions it's aping and with it's newest print extended character levels to 24, which (as Siege also uses character level added to skill rolls) puts 3E bloat back on the menu and functionally destroys the underlying game system around level 15. Possibly earlier, but rolling a d20 and adding 20+ to a roll was always the end of the d20 system. Power levels are also not comparable with B/X so there is no compatibility. This is the OSR's grandpa, and like grandpa, it's seen better days and has some very backwards opinions that you don't want to see live around a dinner table. As it sort of tried to ape B/X mechanics books that are strictly add-on mechanics are fairly compatible with B/X, the best example of which is the now Out of Print Arms & Armor book, which had essentially B/X stats for tons of different historical weaponry and armor throughout history, with artwork showing said items in the case of weapons.
Dungeon Crawl Classics - See here. The modules are mostly OSR compatible, so I still get them, and have a copy of the pre-They/Them corebook with cover art by the great Jeff Easley, so I'd recommend if you're getting in to them only buy DCC modules pre-#100 and their Judges Guild reprints (not revisions, just the four modules they reprinted: Dark Tower, Thieves of Fortress Badabaskor, Tegel Manor, and Citadel of Fire) and their TSR-derived OAR modules (1-6), and Metamorphosis Alpha reprints/supplements if you can find them (good luck).
Dragonslayer - See here. Not much more to say. B/X wannabe by nature of being a Labyrinth Lord wannabe. Technically OSR, but still bad in form and function. If you must, you're better off just getting Barrowmaze Complete. The author shot all of his hot creativity into this megadungeon, his others are all fairly retready, and this game is proof of his empty tank.
Hackmaster 5E - Unlike everything else "5E", this predates D&D5E and therefore is not referencing it. Actually it's referencing that the first edition of the game was 4E, because at the time D&D3E was just coming out so Hackmaster of course had to one-up them. Same is true for 5E. Hackmaster 4E is a parody based on AD&D2E and the long running comic of the creators, Knights of the Dinner Table. Hackmaster 5E is the D&D 3E and 4E that should have been - a cleaned up, streamlined, de-parodied version of Hackmaster 4E with true innovation that has not been duplicated or attempted to be duplicated since. The game is not OSR as it is not compatible with TSR D&D. What it is, is the best edition of D&D that's ever been printed for a hard core RPG enthusiast. A legacy game. The kind of game that actually elevates the genre of roleplaying and requires the players and GM to elevate themselves to even attempt to play it.
Fantastic Heroes & Witchery - Very good gonzo-B/X OSR game. Lots of interesting options, it's a shame Dom disappeared from the material sphere due to some combination of being fucked over by Pundit and being butthurt that his products were taken under the black flag. Still an innovative work deserves mention.
Labyrinth Lord - The original B/X wannabe, created before they knew how litigious WotC would be regarding the OGL, so it takes painstaking steps to not be identical to B/X... to the point that it sucks. OSE is better as a complete copy of B/X and Basic Fantasy is better than both games period, and can use the supplemental material of both games, so why would you even care about the cores? Labyrinth Lord has some of the best supplementation from the early OSR (2006-2014), including Anomalous Subsurface Environment, Red Tide, Stonehell, etc.
Lamentations of the Flame Princess - There is almost nothing worth any merit here. If given a time machine I'd go back and tell myself to buy Broodmother Skyfortress, Qelong, the God that Crawls, Better Than Any Man, and the Goodman Games print of Random Esoteric Creature Generator. There is straight up nothing else worthy of note produced prior to 2018 when I stopped collecting his stuff, and really nothing after. The game is not OSR as while it's got the generic underpinnings of B/X it is not compatible with TSR D&D and vice-versa.
Microlite20 (including all derivatives) - Get everything, it's mostly free. It's also mostly corebooks so if you don't like one don't bother getting the rest. Legit OSR OG though.
Old School Essentials (formerly B/X Essentials) - While it's an utter rip-off of B/X, as in 100% identical mechanically, at least in the "classic" version. It is also ludicrously expensive. Basic Fantasy is miles better. There's a stench of grift on this game line, as the only good design was done by Moldvay likely before the "author" (editor) was born. There are cheaper and better ways to get copies of B/X compiled into one document without any mechanical consideration.
OSRIC - OSRIC is pretty great, it could be greater, but there are elements of AD&D design that need left on the cutting room floor. Basically they need to design an Advanced Fantasy RPG to correspond with Basic Fantasy that highlights the good from AD&D and eliminates the bad. Spoiler alert: It's not the harlot table. Keep that in just to annoy the woke.
Sine Nomine - This guy makes some very interesting tools, well worth the cover price. The games themselves have some hollowness as they remind me of how D&D3E compartmentalizes abilities. True20 might be a closer fit. They read good, but play a little oddly. As such my favorite thing from his catalog continues to be Red Tide and it's supplements, including Scarlet Heroes. Not as a game unto itself mind you. But the tools are interesting when added to a Basic Fantasy campaign.
Sword & Wizardry Complete - It's first two editions were the stuff of OSR legend, but it has since grown into a bloated, awful mess. There was a few harbinger editions (the box edition and the boxed set), but it's clear Matt Finch has flown directly into Cuckooville with emphasis on the "Cuck". As such when referring to S&W complete, the editions produced before 2012 are the only that are considered.
Sword & Wizardry White Box/White Box Fantastic Medieval Adventure Game - S&W is all seemingly in the same woke boat, but luckily FMAG still holds true to the original spirit. Go that route until someone forces the change on FMAG. Then exit entirely.
If your game is not on this list it is probably not an OSR game. Not even a bad one. This includes Shadowdark (not forgetting it's double-excommunicated), all the trash on itch, all the minimalist trash Chris MacDowell writes, Mork Borg, and all derivative works of such.