Crafting the Essentials

The Rules We Need.
There is much discussion among us gamers about "rules". There always has been. The earliest days of the hobby (circa 1975) witnessed many rules related discussions carried out mainly through newsletters (like Alarums & Excursions) and various amateur publications - discussions which gave rise to rule adaptations and eventually whole new games. As a participant who joined the discussion around 1978, I still enjoy talking about rules. What rules do we prefer? What rules are essential to the game we would like to play and what rules seem unnecessary or even undesirable?
Looking at my favorite system, the original three Little Brown Books published in 1974 (which I fondly refer to White Box - my 5th printing came in a white box), I have an abbreviated list of the bare essentials for running my type of game. Obviously a game built for dungeon delving needs a combat mechanic. The original edition refers the reader to a previous wargame called Chainmail, but it also includes the now standard d20 roll high "alternative combat system". Rolling a d20 against a target number (AC) can fill this requirement. Personally, I don't think it matters whether one uses ascending or descending AC or even THAC0 - they are essentially the same.
The core of any role-playing experience is the character(s). Rules for character generation and abilities seem a necessity, but there are many ways to do this. I prefer the simple roll 3d6 in order for the classic six abilities, but any of a number of alternative methods will suffice. I also like to use classes, but those are hardly essential, hence the many classless systems. The original three classes work for me, but that can be easily trimmed to two (fighter, wizard) or expanded with additional "custom" classes designed to perfectly fit a particular setting.
The basic statistics of the class system in the original edition include experience points and level, hit points, and fighting capability for each class. I like saving throws and consider their use essential to my game because they are so useful for determining whether the character is adversely effected by various hazards. A skill system could potentially eliminate the need for saves, however. Some retro-clones have simplified the original saving throw table to a single saving throw number which varies somewhat by character class and level. Essentially, this serves the same purpose, but I rather enjoy using the original five saving throws matrix - death ray or poison, wands including polymorph or paralyzation, stone, dragon breath, and staves & spells. (They just seem to have a bit more nostalgic appeal for me.)
Magic is a defining feature of most fantasy settings. Players enjoy the incorporation of magic spells, magic items and magical creatures. For magic using types the essential rules need to include the basics of how magic will work - not the philosophy of magic, just the game rules. There are less "structured" magic systems and more than that used in the original RPG game, but I am partial to its so-called "Vancian" magic system which combines a simple mechanic with a power limiting factor. Whether one uses the "Vancian" system from D&D or some other rules for magic, this is an essential component of our fantasy rules. Using the "Vancian" system involves a spell level and memorization matrix and a list of spells with brief descriptions. Once you have cast your allotted spells for the day, you have no more until daily renewal.
Monsters and treasure are a part of the game, but as common as fantasy tropes are in today's popular culture, there doesn't need to be extensive lists of these. Everyone who is familiar with FRPGs can generate their own monsters and treasures and these self created, individualized creations are the best and most rewarding to play with anyway. Movement rates are relatively unimportant when using "theater of the mind' play and can be glossed over if desired. Lastly, guidelines for awarding experience should be established. Earning experience is often what motivates player behavior.
In summary, the essential rules for a White Box style game include a combat system that gives us the rules for how to hit and damage enemies in a fight. Character generation rules seem necessary for creating our player characters - two classes, fighting types and casting types, will suffice. Also required is a magic system - which may involve the largest portion of the rules as written in a fantasy genre. Magic is often what flavors a setting and crafting the magic system carefully will pay dividends in play. A method for awarding experience and leveling up characters is central to the classic RPG and players may expect it, but the game can be enjoyed for some time using only characters as they are initially rolled up. After all, it's the fun of "finding out through play", exploring, discovering, solving, surviving and acquiring that keeps us coming back to the table for more.