So on the weekends, Chainmail was our go-to game. My personal favorite section is the Jousting Table. If you don't have a lot of time, The Jousting Table is always there. It's a diceless system made up of a simple pair of tables and a shield schematic. Pick a position and target, compare and there are your results.
Being my dad, we had 25 mm figures for every entrant in the Tourney. Even better, my dad cribbed lines from books and movies like Ivanhoe, The Lone Ranger, and an amazing number of Errol Flynn movies. The results were not simply "kill", "unseated", etcetera. It was a full-on color commentary on the action. More akin to hockey than jousting.
Every once in a while, I like to throw a wildly different mechanic at my players. The more complex the rule system, the harder it is to integrate a completely new mechanic. I have simply written ruleset for sprinting, I call it the Movement Game. It is less than one page long, has a picture or two to help, and is largely based on AD&D's regular movement system. It is also remarkably non-lethal and covers a range of scenarios. The danger of it is players will try to invoke it when things go to hell in combat. It's relatively harmless when player-invoked.
I probably came up with it while thinking about the Jousting Table from Chainmail. Instead of a table, every character has a figure or chit and can move an inch, one right after the other. Dirt simple.
For my next session in November, I am brainstorming a mechanic called "Evil Eye". A character who has the center position on a gameboard can impose a status effect like "freeze", "fall" or "flee" on enemies. The central player can only affect a 30-degree arc of the playing area, so keeping enemies away is difficult because the players are surrounded. Exactly who is giving the orders really depends on the party, who realizes the center of the board is important, etc. So it could be the Super Amadeus Arch-Machiavellian... or the cook he hired.
It's so much fun to bring something simple to the table.