Is it S&W? LL? Something else?

What game has the essence of D&D distilled down into its rawest form?

Moldvay's Basic.  Reprints are available on DTRPG

Swords & Wizardry Whitebox

You can download the PDF for free.

How does Moldvay Basic differ from Red Box, and from S&W White Box/0e?

Quote from: Benoist;656413Swords & Wizardry Whitebox

You can download the PDF for free.

I keep forgetting that S&W is simpler to use than OD&D

Quote from: 1989;656416How does Moldvay Basic differ from Red Box, and from S&W White Box/0e?

S&W Whitebox basically streamlines the OD&D 1974 rules and interprets whatever was confusing, implicit, or otherwise omitted from the rules to create a single coherent interpretation out of it (excising references to chainmail, making the d20 roll the sole mechanic of combat, instead of the alternate to Chainmail's 2d6 man-to-man combat, etc).

So, unlike OD&D, you've got a game that's straightforward right out of the box, though it does lose some of its initial magic IMO, because of the confusion and omissions that got streamlined into a precise, kind of bland interpretation first, but also because the greater part of the third volume of the original system, The Underworld and Wilderness Adventures, has not been replicated by the clone, including some of its most wacky (awesome) rules like the knights attacking parties around their keep in the wilderness and stuff like this.

So in other words, S&W Whitebox is a particular interpretation of OD&D rules. The main components are obviously there: three classes (fighting man, magic user and cleric), d20 roll versus AC (descending or ascending, your choice), d6 damage for all weapons, and so on. It's easily the simplest expression of the D&D rules out there, bar none, and it's kind of liberating in a way more convoluted versions of the game aren't, in the sense that you really can take the game and its rules in any direction you want while starting from a very simple framework in your campaign.

Are you counting internet pdf freebies?  If so, I'd say some version of Microlite20, or even better, Searchers of the Unknown and maybe the spellcaster and demihuman supplements.

Searchers of the unknown is the simplest version that I have played.

Microlite 20 also gets pretty simple. Despite technically being based on d20 instead of older D&D, it feels much more like TSR D&D. There's only three abilities and four skills, saves are essentially the 3e ones (one per ability score,) spells have one-line descriptions and cost spell points equal to spell level +1, and modifiers are decided on a case-by-case basis by the GM and are limited to +/- 1 or 2. No feats, no lengthy rules, and classes/races are minimalist in spirit. There are many variants built off that structure, including Microlite74 which attempts to hew closer to the OD&D approach.

Personally, I prefer my OD&D house rules, but it's an intriguing alternative.

Microlite74, if "available as a free pdf" counts as "in print".

20's alright and all but you do kind of need access to the SRD to make the most of it.

Searchers of the Unknown, unless you're short a printer and one sheet of paper.

I find that the older I get, the less rules I want.

*Optional* rules and systems and lists and tables . . . yeah, I like that, if I can pick and choose, but I really seem to like the most simplest of cores.