Some games have really great subsystems and mechanics that can be used in other games. What's your favorite? How do you adapt it?
13th Age Montage Scenes: I run those in any system that has any form of checks. If the system has a meta-currency, I'll use a montage scene to refresh them, but it's trivial to run anywhere.
The One Ring Travel System: The core elements I use are (1) each player takes one of a set of roles (2) Guide rolls to see how far you get before an event (3) roll randomly to see which other role the event occurs to. I choose a system-specific check for the player and if it fails, something bad (over the scale of a several days journey) happens. If the system has a fatigue score, use that, or add a sticky aspect, or a Yellow King condition. Whatever the game system has as a multi-scene penalty
4th Edition Skill Challenges: Everyone uses these nowadays, so many don't even think of it as 4E specific: To achieve a goal, need X successes before Y failures. Skills get different DCs depending on how applicable they are. Fails usually have some other minor consequences. Some skills "unlock" other skills at lower DCs. This is how I almost always resolve social scenes where there is a clear objective -- I'm with
@Umbran in not generally liking a single roll to resolve social encounters in a system where combat needs many.
Fate Advantages: Rather than just an immediate +X bonus for assisting someone else, as most games have, throw out a card with the same +X bonus, but give it a name and allow anyone to use it. Much more flavor and more useful as, for example, a floating +2 you can apply AFTER you see the roll is quite strong in a d20 game.
Don't Rest Your Head: Also in Aliens game more recently. The basic idea is you get to roll more dice, but the extra dice allow bad things to happen. One easy use is to ask a player if they want a safe +2 bonus, or to roll a +d6 bonus, but if a 1 comes up on it there will be a complication.
CoC Sanity: Been adding this to horror sessions of other games for years. In AD&D I used SAN = WILL + CHA - INT because batty wizards is very in-genre and Conan resists horror very well. Lose it when bad stuff happens, get below half and you take an in-game consequence, lose it all and you are out for the scenario.
Bloodied: I used the 4E concept of being at half hits or lower is a pre-requisite or trigger for abilities all the time. Much nicer for dragon breath recharge than rolling d4 as it usually means 2 breaths per fight, which seems about right for me. Good for solos where you are worried the players may gank the solo before their cool power is loosed.