Something that is not explicitly in B/X are ability checks and Save Throws for mundane things. I am just noting it down here so I remember to put in the rules specifically, as I have a habit of just making assumptions that folks would know these things. I use both prolifically and plan to do in Valley of Blue Snails.
Ability Checks will cover actions which the PC intitated. Save Throws will cover events that occur to the PCs that are out of their control.
Abilities checks will be used for actions which have a moderate chance of failure. These are usually actions the PCs have initiated intentionally in most cases. Want to mop your floor? no check needed. Want to climb a fence before the guard dogs get you? check needed. This will cover the crazy things PCs try to do, as well skills that the PC may know. I see no need for alist of skills in the game since ability checks and PCs background should cover it all. Probably anyone who is reading this will know how to perform an ability check but let me spell it out just in case.
Roll 1d20. If the number is equal too or less than the abilities that is being tested, the action is considered a success. For example, lifting a iron gate would require a strength check. Recalling the linage of a local lord would require a Intelligence check. Charming a reeve who is questioning you about a weapon that is not peace-bonded will require a Charisma check (and role-playing of couse). And so on and so forth.
These can rolls can be modified based on the difficulty, or the roll will simply not be allowed if the DM deems it impossible. Modifiers would not go beyond +4 to -4, and honestly I don't bother to use them much. A natural 1 or natural 20 I deem as dismal failure or great success.
Save Throws I use for mundane things that are usually out of the PCs control. If they are tossed in freezing water I may allow a Save vs Petrification to see how well they react. If a bar tender tosses a PC out of a window, I may allow a Save vs Wands to avoid damage. Attempting to out drink the town drunk would require a Save vs Poison, etc. Really its just another random event to see how the PCs luck is going. I like it because unexpected things can happen and the story is not so driven by the DM and fate get a hand in there too.
Save Throws can likewise be modified to +4 to -4. Save throws are more difficult to succeed, especially at the early levels. So it is important to keep in mind of the reprecutions of failing a saves, because it will probably happen. If this mechanic is used routinely the PC should notice they are noticeable getting more 'heroic' as they level up.
Otter mentioned in Tunnels and Trolls that PCs get experience when they make a succesful Ability Check or Save Thrown. I like this idea and will probably use it since it promotes trying stuff. I will talk about that more tomorrow however when I devote some time to XP.