Researching the world of tabletop gaming I became entranced by elegance with which some of them create experience with very limited set of mechanics. While digital gaming does all the math for you instantly, offers a list of options for the next action, board games can't have players look all over the board, consulting the manual and doing addition in their mind just to know if they can do something or not. While it is tempting to think that all those limitations result in detrimental experience, it would be wrong as tabletop setup is an excellent opportunity to see if mechanic can be engaging. Making a game out of tangible things, easily readable elements ensures that everything is connected in intuitive way. Digital game continues no matter if player understands it or not, engaged or not. Before moving a figurine from grid cell A to grid cell B you should make sure that it is not against the rules. Ok, I think I made my point, lets get to ideas I want to remember:
MODIFY A SET OF RANDOM ELEMENTS
If you try to upgrade your character/army/whatever with cards, each adding/subtracting a stat you inevitably end up with too much math to do. Tabletop often resorts to modifying a set of cards by adding better cards in there. Deck building games are made around that idea, but it also can be used to fulfil a secondary role. Monopoly has a similar concept: instead of adding cash every turn, you increase chance of getting cash.
It is always more fun when instead of taking turns the event happens in an instant. For example: "two players rolling a dice and the one with higher number wins" is more fun then Player 1 rolls the dice, resolves his result, then player two rolls his dice.
For player's strategy some actions are more critical then others. It is best when rules accommodate the "I need to get this done no matter the cost" panic and have rules that allow to perform otherwise suboptimal actions, sacrificing more resources to get something done.
NO ROLEPLAY STATS
While Strength, Wisdom, Charm etc. are as common as a goblin in any Lvl 1 dungeon, they better not be your first pick. There is nothing wrong about those in particular, but equivalent stats in general that do little to make things more interesting and more to complicate the math. "Statistic A lets you play actions X while statistic B lets you play actions Y". As much as numbers don't add much fun, different group of numbers are just as useless.
TURNS AFFECT EVERYONE
During one player's turn he may select an action everyone takes. So waiting for another player is never active. Think Starlight Imperium.
Can be great balancing force. Usually it is a choice between increasing your power and getting points. So getting a victory point sets the player back a bit.
Any mechanics that make choice easier are always welcome. For example, allowing to use the buff only when you know if you need it or not.