My two favorite editions of D&D (that I've actually gotten to run; OD&D might take precedence if I ever find someone willing to play it) are Moldvay Basic/Cook & Marsh Expert (B/X), and AD&D 2nd Edition. These two iterations of the game share some common features. Both are fairly tightly written; both focus on core classes while still giving a few additional options for more non-conformist players; and both have a good deal of rules clearly marked as optional.
At the same time, there is a distinction in my mind between optional rules, tournament rules, and variant rules. The first can be completely excluded from the game without having too many adverse effects (unless the DM or players prefer to use said rules). The second, mostly a feature of AD&D2, set out rules that are used in place of the "optional rule" to allow for greater consistency at events and organized play. An example of this would be the two different sets of rules for encumbrance (in the PHB) and aerial combat (in the DMG); in the latter case, the "tournament rule" is the standard abstraction of passes and movement classes, while the "optional rule" requires the use of miniature figures or markers - to my recollection, the only AD&D2 rule to explicitly require them.
The third category consists of a different way of doing an integral rule. For instance, initiative is an essential part of combat; no matter what system is used for it, a system is necessary. Both B/X and AD&D2 have simple group initiative as the default rule; individual initiative, while marked as optional, is more of a variant rule because it replaces an existing system with a different way of doing the same thing. (AD&D2 also has a mix between these, referred to as "group initiative" - as opposed to "standard initiative" - that still divides battles into sides, but uses a small table of modifiers for which every member of a side must qualify.)
Likewise, weapon damage (in B/X, at least) can be handled in one of two ways. The standard rule is to simply use 1d6 for all character attacks; although it isn't explicitly stated, one assumes that monster attacks would function similarly, as they indeed did in OD&D. The table of variable weapon damage is a variant rule; damage is still calculated and implemented as normal, but the die rolled is different.
To anyone reading this post: what are some of your favorite (or least favorite) variant and optional rules in D&D or similar games?